of  California, 

FROM    THi:    I.IUKAKV    t  >F 

DR.     FRANCIS     LIEBER, 
or  of  History  and  Law  in  Columbia  C'']K"_'<\  N<-\v  York 

T^E  GIFT   OF 

MICHAEL     REESE, 

Of  SUM  Franciscd. 

1 S  7  3  . 


THE 

CABINET 

OF 

NATURAL  PHILOSOPHY. 

CONDUCTED    BY   THE 

REV.  DIONYSIUS  LARDNER,  LL.D.  F.R.S.  L.&E. 

M.R.I.A.  P.R.Ast.S.  F.L.S.  F.Z.S.  Hon.  F.C.P.S.  &c.  &c. 
ASSISTED    BT 

EMINENT  SCIENTIFIC  MEN. 


HYDROSTATICS 

AND 

PNEUMATICS. 

BY 

THE  REV.  DIONYSIUS   LARDNER. 
WITH  NOTES 

BY 

THE  AMERICAN  EDITOR. 


PHILADELPHIA ". 
CAREY  AND  LEA— CHESTNUT  STREET. 

1832. 


TREATISE 


ON 


HYDROSTATICS 

AND 

PNEUMATIC  S  . 

BY   THE 

REV.  DIONYSIUS   LARDNER,  LL.D.  F.R.S 
JFfvst  Shnerfcan,  from  t$e  Jffrst  Hontroti  35faftfon. 

WITH  NOTES, 

BY 

BENJAMIN  F.  JOSLIN,  M.  D 

PROFESSOR   OF   NATURAL    PHILOSOPHY   IN    U1UON   COLLEGE. 


CAREY  AND  LEA— CHESTNUT  STREET. 


CONTENTS. 


HYDROSTATICS. 

CHAP.  I 

INTRODUCTION. 

Division  of  the  physical  Forms  of  Matter.— The  solid  and  liquid  States.— Cohe- 
sion.— Repulsion. — Heat. — Subject  of  Hydrostatics Page  1 

CHAP.  II. 

PRESSURE    OF    LIQUIDS. 

Pressure  transmitted  equally  in  all  Directions. — Experimental  Proof  of  this. — A 
Liquid  is  a  Machine. — Hydrostatic  Paradox. — Bramah's  Hydrostatic  Press. — 
Hydrostatic  Bellows. — Various  useful  Applications  of  this  Property. — Means  of 
transmuting  Signals. — Dr.  Arnott's  Suggestion  of  its  Application  in  surgical 
Cases  — Illustrations  from  the  Animal  Economy. — Circulation  of  the  Blood.  .  3 

CHAP.  Ill 

OF    THE    PRESSURE    PRODUCED    BY    THE    WEIGHT    OF    A   LIQ.UID. 

Pressure  proportional  to  the  Depth. — Pressure  on  the  horizontal  Bottom  and  per- 
pendicular Sides  of  a  Vessel.— Experimental  Proofs  of  the  Property. — Total 
Pressure  on  the  perpendicular  Sides  of  a  Vessel  computed. — Embankments, 
Dams,  and  Floodgates. — Method  of  computing  the  total  Pressure  on  the  Surface 
of  a  Vessel  of  any  Shape. — Examples. — Globe. — Cube. — Various  Effects  pro- 
duced by  the  Pressure  of  Liquids  at  great  Depths. — Cork  forced  into  a  Bottle. — 
Water  forced  into  the  Pores  of  Wood. — Liquids  not  absolutely  incompressible. 
— Experiment  to  prove  this 17 

CHAP.  IV. 

LIQUIDS    MAINTAIN    THEIK   LEVEL. 

Experimental  Proofs. — Vessels  connected  with  communicating  Tube. — Several 
Vessels  between  which  there  is  a  free  Communication. — Hydrostatic  Paradox 
explained  by  this  Principle. — Surface  of  a  Liquid  level. — Why  the  Quality 
does  not  extend  to  Solids. — Surface  of  the  Land. — Surface  of  the  Sea. — Curious 
optical  Deception  in  Waves. — Similar  Property  in  revolving  Screw. — Ornamen- 
tal Fountain  Clocks.— Phenomena  of  Rivers,  Springs,  Wells,  Cataracts,  explain- 
ed.— Canals,  Looks. — Method  of  supplying  Water  to  Towns. — Exact  Sense  of 
the  word  Level. — Common  Surface  of  two  Liquids  in  the  same  Vessel. — Level- 
ing Instruments. — Spirit  Level 37 


Vl  CONTENTS. 

CHAP.  V. 

OF    THE    IMMERSION    OF    SOLIDS    IN    LIQUID! 

To  determine  the  exact  Magnitude  of  an  irregular  Solid.— When  soluble  in  the 
Liquid. — When  porous. — Effect  on  the  apparent  Weight  of  the  Liquid. — Effect 
on  the  apparent  Weight  of  the  Solid.— The  real  Weight  of  the  Solid  and  Liquid 
not  changed  by  Immersion. — Cause  of  the  apparent  Change. — When  a  Body  is 
suspended. — Floating  Bodies. — These  Properties  deduced  from  the  fundamental 
Principles  of  Hydrostatics. — The  same  Solid  sinks  in  some  Liquids  and  rises  in 
others. — Buoyancy. — Its  Effects  in  submarine  Operations. — Its  Effects  perceiv- 
able in  Bathing. — Boats  may  be  formed  of  any  Material,  however  heavy.— An. 
Iron  Boat  which  cannot  sink. — Method  of  preventing  Ships  from  foundering. — 
Effects  of  the  Cargo. — Ball  Cock,  and  other  floating  Regulators. — Means  of 
raising  Weights  from  the  Bottom  of  the  Sea. — Method  of  lifting  Vessels  over 
Shoals.— Life  Preservers. — Swimming. — Water  Fowl. — Fish. — Why  a  drowned 
Body  floats.— Philosophical  Toy.— Why  Ice  floats.— Rocks  raised  to  the  Sur- 
face by  Ice , ,  ..,,,,.  53 

I 

CHAP.  VI. 

OF    DIFFERENT   LIQUIDS    IN   COMMUNICATING    VESSELS. 

Lighter  Liquids  float  to  the  Top. — Oil,  Water,  and  Mercury. — Cream  of  Milk. — 
Ingredients  of  the  Blood.— Oil  and  Spirits,— Proof  Spirits.— Water  and  Wine.— 
Water  in  the  Depths  of  a  frozen  Sea  less  cold  than  at  the  Surface.— A  Liquid 
may  boil  at  the  Surface,  while  the  lower  Parts  are  cold.— Method  of  applying 
Heat  to  boil  a  Liquid. — Method  of  applying  Ice  to  cool  Wine.— Different  Liquids 
in  a  bent  Tube.— Method  of  raising  Water  by  impregnating  it  with  Air.  ..  83 

CHAP.  VII. 

EQUILIBRIUM    OF    FLOATING   BODIES. 

Conditions  of  Equilibrium.— Cases  of  Stable,  Instable,  and  Neutral  Equilibrium.— 
Experimental  Proof.— Feat  of  walking  on  the  Water — Life  Preserver — Stabil- 
ity of  Ships. — Position  of  Cargo. — Ballast. — Danger  of  standing  up  in  a  Boat. — 
Inclination  of  a  sailing  Vessel. — How  avoided  in  Steam  Vessels 91 

CHAP.  VIII. 

SPECIFIC    GRAVITIES. 

Different  Senses  of  the  Terms  Heavy  and  Light. — Weight  absolute  and  relative. — 
Specific  Gravity. — Standard  of  Comparison  for  Solids  and  Liquids. — For  Gases. 

Density. — The  Immersion  of  Solids  in  Liquids  gives  their  Specific  Gravities. 

Methods  of  ascertaining  Specific  Gravities. — Hydrostatic  Balance. — Sikes's 

Hydrometer.— Nicholson's  Hydrometer.— De  Parcieux's  Hydrometer.— Method 
of  determining  the  Constituent  Parts  of  Compound  Bodies. — Alloys  of  Metal. — 
Spirits. — Adulteration  of  Milk  and  other  domestic  Liquids. — Hiero's  Crown. — 
Penetration  of  Dimensions 109 


CONTENTS.  VII 

CHAP.  IX. 

HYDRAULICS. 

Velocity  of  Efflux  from  an  Aperture  in  a  Vessel. — Proportional  to  the  Depth  of  the 
Aperture.— Equal  to  the  Velocity  acquired  in  falling  through  that  Depth.— 
Effect  of  atmospheric  Resistance. — Vena  Contracta. — Rate  at  which  the  Level 
of  the  Water  in  the  Vessel  falls. — Lateral  Communication  of  Motion  by  a 
Liquid. — River  flowing  through  a  Lake. — Currents  and  Eddies. — Effects  of  the 
Shape  of  the  Bed  and  Banks  of  a  River.— Force  of  a  Liquid  striking  a  Solid,  or 
vice  versfr. — Effect  of  an  Oar. — Wings  of  a  Bird. — Direction  of  the  resisting  Sur- 
face.— Effect  of  the  Velocity  of  the  striking  Body. — Solid  of  least  Resistance. — 
Shape  of  Fishes  and  Birds.— Speed  of  Boats  and  Ships  limited.— Comparative 
Advantages  of  Railroads  and  Canals ,  .  130 

CHAP.  X. 

OF    HYDRAULIC    MACHINES. 

Water  Wheels. — Overshot. — Undershot. — Breast. — Barker's  Mill. — Archiraedei' 
Screw.— Sluica  Governor.— Chain  Pump ,  ,  ,  ,  ,  150 


PNEUMATICS 


CHAP.  I. 

INTRODUCTION. 

Form  of  Bodies.— How  affected  by  Heat — Aeriform  State — Elasticity.— Division 
of  mechanical  Science  — Compressibility  and  Incompressibility. — Permanently 
elastic  Fluids.— Vapor — Steam.— Atmospheric  Air *  ....  169 

CHAP.  II! 

PROPERTIES    OF    ATMOSPHERIC    AIR. 

Atmospheric  Air  is  material.— Its  Color.— Cause  of  the  blue  Sky.— Cause  of  the 
green  Sea. — Air  has  Weight.— Experimental  Proofs. — Air  has  Inertia. — Exam- 
ples of  its  Resistance. — It  acquires  moving  Force. — Examples  of  its  Impact. — 
Air  is  impenetrable.— Experimental  Proofs 174 

CHAP.  III. 

ELASTICITY    OF    AIR. 

Elastic  and  compressing  Forces  equal. — Limited  Height  of  the  Atmosphere. — 
Elasticity  proportional  to  the  Density. — Experimental  Proofs. — Internal  and 
external  Pressure  on  close  Vessels  containing  Air 181 


Vlll  CONTENTS. 

CHAP.  IV. 

V.'EIOHT    OF    AIF. 

Maxim  of  the  Ancients. — Abhorrence  of  a  Vacuum, — Suction. — Galileo's  Investi- 
gations.— Torricelli  discovers  the  atmospheric  Pressure. — The  Barometer. — 
Pascal's  Experiment. — Requisites  for  a  good  Barometer.— Means  of  securing 
thenu — Diagonal  Barometer. — Wheel  Barometer. — Vernier. — Uses  of  the  Ba- 
rometer.—Variation  of  atmospheric  Pressure.— Weather  Glass.— Rules  in  com- 
mon Use  absurd. — Correct  Rules. — Measurement  of  Heights. — Pressure  on 
Bodies. — Why  not  apparent.— Effect  of  a  Leather  Sucker. — How  Flies  adhere 
to  Ceilings,  and  Fishes  to  Rocks. — Breathing. — Common  Bellows. — Forge 
Bellows. — Vent-Peg. — Tea-Pot. — Kettle. — Ink-Bottles. — Pneumatic  Trough. — 
Gpggling  Noise  in  decanting  Wine 188 

CHAP.  V 

RAREFACTION    AND    CONDENSATION    OF    AIR. 

Exhausting  Syringe. — Rate  of  Exhaustion. — Impossible  to  produce  a  perfect 
Vacuum. — Mechanical  Defects. — The  Air  Pump. — Barometer  Gauge. — Siphon 
Gauge. — Various  Forms  of  Air  Pump. — Pump  without  Suction  Valve. — Exper- 
iments with  Air  Pump. — Bladder  burst  by  atmospheric  Pressure. — Bladder  burst 
by  Elasticity  of  Air. — Dried  Fruit  inflated  by  fixed  Air. — Flaccid  Bladder  swells 
by  Expansion. — Water  raised  by  elastic  Force. — A  Pump  cannot  act  in  the 
Absence  of  atmospheric  Pressure. — Suction  ceases  when  this  Pressure  is  remov- 
ed.— The  Magdeburg  Hemisphere. — Guinea  and  Feather  Experiment. — Cupping. 
—Effervescing  Liquors. — Sparkling  of  Champagne,  &c. — Presence  of  Air 
necessary  for  the  Transmission  of  Sound. — -The  Condensing  Syringe. — The  Con- 
denser  , .214 


CHAP.  VI. 


MACHINES  FOR  RAISING  WATER* 

The  Lifting  Pump. — Pump  without  Friction. — The  Suction  Pump. — The  Forcing 
Pump. — The  same  with  Air  Vessel. — The  same  with  a  solid  Plunger. — Double 
Forcing  Pump. — The  Fire  Engine. — Siphon. — The  Wurtemburg  Siphon.  .  .238 

CHAP.  VII 

THX    AIR   GUN,    AIR   BALLOON,    AND    DIVING    BELL. 

Tha  Air  Gun. — First  Attempts  at  Balloons. — Lana's  Balloon  of  rarefied  Air. — 
Fire  Balloons.— Montgolfier's  Balloon.— First  Ascent.— Balloons  inflated  with 
Hydrogen. — Parachute. — Blanchard's  Experiment. — Causes  of  the  Efficacy  of 
the  Parachute. — Ascent  of  Gay-Lussac  and  Biot. — Appearances  in  the  higher 
Regions  of  the  Atmosphere. — The  Diving  Bell 257 


A 
TREATISE 

ON 


HYDROSTATICS- 


CHAP,  i. 

INTRODUCTION. 

DIVISION  OF  THE  PHYSICAL  FORMS  OF  MATTER.  —  THE  SOLID  AND 
LIQUID  STATES. — COHESION.  —  REPULSION. —  HEAT. — SUBJECT  OF 
HYDROSTATICS. 

(].)  To  investigate  and  explain  the  phenomena  of  nature, 
and  to  exhibit  with  clearness  and  perspicuity  the  laws  which 
prevail  among  them,  it  is  necessary  to  group  the  objects  and 
appearances  which  are  under  consideration  in  classes  distin- 
guished by  definite  lines  of  separation.  This  system  ought, 
however,  to  be  regarded  as  artificial,  and  adopted  as  an  aid  to 
the  limited  powers  of  the  human  mind,  rather  than  as  corre- 
sponding to  the  actual  state  of  the  natural  world.  Material 
substances,  and  the  various  relations  which  are  developed  by 
their  mutual  agency,  exist  separately  and  individually  ;  science 
arranges  them  in  .classes,  according  to  certain  similitudes  and 
analogies  which  are  observed  among  them ;  but  this  classifica- 
tion is  often  to  a  great  extent  arbitrary,  and  the  individuals  of 
one  class  are  by  imperceptible  degrees  shaded  off  into  those 
of  another,  like  the  languages,  manners,  and  habits  of  adjacent 
countries 'between  Avhich  no  natural  boundary  is  placed.  It 
must  be  admitted  that,  under  such  circumstances,  classification 
does  a  violence  to  nature  ;  but  yet  the  aids  which  it  affords  to 
the  investigation  of  her  laws,  and  the  impulse  which  it  gives 
to  the  general  progress  of  discovery,  are  advantages  which 
outweigh  the  objections  which  lie  against  it. 

The  division  of  bodies,  or  rather  of  the  physical  states  in 
which  bodies  are  found,  into  solid  and  fluid,  suggests  these 
reflections.  Two  opposite  influences  are  observed  to  pervade 


%  A    TREATISE    ON    HYDROSTATICS.  CHAP.    1. 

the  material  world.  The  cohesive  principle  is  one,  in  virtue 
of  which  the  component  particles  of  all  bodies  have  a  tendency 
to  collect  and  consolidate  themselves  into  hard  and  dense 
masses.  This  principle  is  opposed  by  one  of  a  contrary  nature, 
which  generally  seems  to  be  connected,  if  not  identical,  with 
that  of  heat.  By  virtue  of  this  latter,  the  elementary  molecules 
of  the  body  which  it  pervades  have  a  disposition  to  separate, 
fly  asunder,  or  repel  each  other.  In  different  bodies  these  two 
opposing  forces  have  different  relations,  upon  which  the  physical 
state  of  the  body  depends.  If  the  cohesive  influence  predom- 
inate over  the  repulsive  in  any  considerable  degree,  the  par- 
ticles of  the  body  are  held  together  in  a  solid  concrete  mass, 
not  separable  by  any  force  less  in  amount  than  that  by  which 
the  cohesive  attraction  which  binds  the  particles  together 
exceeds  the  repulsive  force  which  tends  to  separate  them.  If, 
on  the  contrary,  these  two  principles  have  an  opposite  relation, 
and  the  repulsive  force  which  gives  the  particles  a  disposition 
to  fly  asunder  prevail  over  the  cohesive  force,  then  the  ele- 
mentary parts  of  the  body  will  separate  indefinitely,  and  dilate 
and  spread  themselves  through  any  vacant  space  to  which  they 
have  free  access.  Such  is  the  case  with  atmospheric  air,  and 
all  other  bodies  existing  under  the  gaseous  form.  Between 
these  two  opposite  states  there  are  an  infinite  variety  of  others, 
corresponding  to  all  the  possible  relations  which  can  subsist 
between  the  cohesive  and  repulsive  forces.  Nevertheless  there 
is  but  one  intermediate  state  which  is  distinctly  recognized  in 
mechanical  science,  to  explain  which  it  will  be  necessary  to 
take  into  consideration  another  force,  viz.  the  gravity  of  the 
component  particles.  A  body  is  said  to  be  solid  when  the 
cohesive  force  by  which  its  particles  are  held  together  is  not 
only  sufficiently  powerful  to  neutralize  the  repulsive  force  which 
may  tend  to  separate  them,  but  also  to  resist  the  tendency  which 
they  have  to  fall  asunder,  like  the  grains  of  a  mass  of  sand,  by 
their  own  weight.  If  this  be  the  case,  the  body,  placed  upon  a 
level  plane,  or  enclosed  in  a  vessel  sufficiently  large  to  contain 
it,  will  maintain  its  figure ;  nor  will  its  projecting  corners  or 
protuberant  angles  drop  off  in  obedience  to  their  gravity,  but 
will  be  held  firm  in  their  relative  positions.  If,  however,  the 
cohesive  force,  though  sufficient  to  prevent  the  separation  of 
the  constituent  particles  of  a  body  by  reason  of  the  repulsive 
force  which  depends  on  the  presence  of  heat  or  any  other  cause, 
yet  be  unable  to  prevent  their  falling  asunder  by  their  own 
weight,  then  the  mass  of  the  body,  if  it  were  placed  upon  a 
plane,  would  be  scattered  over  the  surface  by  the  unresisted 
tendency  which  the  particles  have  to  fall  asunder  by  their 
gravity  ;  and  if  the  body  were  placed  in  a  vessel  which  by  its 
sides  would  restrain  the  particles,  they  would  then  fall  into 


CHAP.    II.  TRANS-MISSION    OP    PRESSURE.  3 

every  cavity  of  the  vessel,  and,  all  the  lower  parts  being  filled, 
the  upper  part  of  the  mass  would  settle  itself  into  a  level  sur- 
face. Such  is  the  case  of  water,  and  all  other  bodies  in  the 
liquid  form.  There  are,  however,  various  states  between  this 
of  decided  liquidity,  and  that  already  described  of  decided 
solidity.  The  gradual  transition  of  glue  from  the  solid  state  to 
the  soft  and  viscid,  and  finally  to  the  perfect  liquid,  will  eluci- 
date these  observations.  The  division  of  mechanical  science, 
on  which  we  are  now  about  to  enter,  is  confined  to  the  con- 
sideration of  bodies  in  a  perfectly  liquid  state  ;  and,  as  water 
has  been  assumed  as  the  type  of  all  other  liquids,  this  division 
of  the  science  has  been  called  HYDROSTATICS.* 


CHAP.  II. 

PRESSURE   OF   LIQUIDS. 

PRESSURE  TRANSMITTED  EQUALLY  IN  ALL  DIRECTIONS. — EXPERI- 
~MENTAL  PROOF  OF  THIS. — A  LIQUID  IS  A  MACHINE. — HYDROSTATIC 
PARADOX. — BRAMAH'S  HYDROSTATIC  PRESS. — HYDROSTATIC  BEL- 
LOWS.— VARIOUS  USEFUL  APPLICATIONS  OF  THIS  PROPERTY. — 
MEANS  OF  TRANSMITTING  SIGNALS. — DR.  ARNOTT;S  SUGGESTION  OK 
ITS  APPLICATION  IN  SURGICAL  CASES.— ILLUSTRATIONS  FROM  THE 
ANIMAL  ECONOMY. — CIRCULATION  OF  THE  BLOOD. 

(2.)  THE  most  striking  of  those  qualities  of  bodies  which 
depend  on  the  fluid  state,  and  that,  indeed,  by  which  this  state 
is  mainly  distinguished  from  the  solid,  is  the  power  to  transmit 
pressure  equally  in  every  direction.  In  mathematical  treatises, 
this  property  is  usually  taken  as  the  definition  of  fluidity,  and 
as  the  basis  of  the  reasoning  by  which  the  whole  superstructure 
of  the  science  is  raised. 

Fig.  I. 


*  The  terms  hydrodynamics  and  hydraulics  are  used  to  express  certain  division! 
of  the  science,  "it  will  be  convenient,  however,  in  the  present  case,  to  embrace 
the  whole  under  the  titlo  Hydrostatics. 


A    TREATISE    ON    HYDROSTATICS.  CHAP     H 

the  ' 


every  part  of  thVn  PrGSSUre  w      be  transmitted  to 


and  a  force  tending  to  burst  the  vessel  wiU  be  produced  thP 
total  amount  of  which  will  be  as  many  pounds^  ^  there  are 
square  inches  in  the  inner  surface  of  the  vessel.  If  the  whole 
mner  surface  of  the  vessel  amounted  to  10,000  square  inches 
then  a  pressure  of  one  pound  on  the  piston  would  produce  a 


to  be 
Fig.  2. 


the  vesfi!     e  apeUreS     ' '  and  erery  P^rt of 


CHAP.  II.  TRANSMISSION  OF  PRESSURE.  5 

a  pound.  Now  suppose  the  piston  P'  to  press  upon  the  surface 
of  the  water  with  a  force  greater  than  a  pound,  then  the  piston 
P7  will  descend  in  the  cylinder,  and  the  piston  P  will  rise. 
Thus  it  appears  that  the  force  of  one  pound  acting  at  P  trans- 
mits to  P'  a  pressure  which  is  unable  to  resist  a  force  greater 
than  a  pound.  From  these  two  experiments  it  appears  that  the 
pressure  transmitted  to  P/  is  neither  greater  nor  less  than  a 
pound,  and  is  therefore  equal  to  a  pound. 

This  may  further  be  verified  by  loading  the  piston  P;  so  as  to 
exert  upon  the  liquid  a  pressure  amounting  to  one  pound.  It 
will  then  be  observed  that  the  pistons  will  just  balance  one 
another.  In  general  it  will  be  observed,  that  so  long  as  the 
two  pistons  are  equally  loaded,  whatever  be  the  amount  of  the 
force  acting  on  them,  they  will  balance  each  other,  and  neither 
will  be  displaced  ;  but  at  the  moment  when  any  force  is  given 
to  one  greater  than  that  which  acts  upon  the  other,  however  in- 
considerable the  excess  may  be,  that  which  is  urged  by  the 
greater  force  will  descend,  and  will  transmit  a  force  to  the  other 
which  will  compel  its  ascent. 

It  therefore  appears  that  any  force  whatever,  which  acts 
upon  a  square  inch  of  the  surface  of  the  water  at  P,  pressing  it 
inwards,  will  produce  an  equal  force  upon  the  square  inch  of 
surface  forming  the  base  of  the  piston  P',  tending  to  force  it 
outwards.  It  is  evident  that  this  would  be  equally  true  if  tiie 
surface  which  forms  the  base  of  the  piston  Pf  were  a  part  of  the 
inner  surface  of  the  vessel,  and  that  no  aperture  or  cylinder 
existed  at"  O'.  It  is  also  evident  that  the  same  results  would 
be  obtained,  in  whatever  part  of  the  vessel  the  aperture  O  might 
be  placed ;  and  therefore  we  infer  that  every  separate  square 
inch  of  surface  receives  from  the  liquid  in  contact  with  it  a 
pressure  equal  in  amount  to  the  pressure  which  is  exerted  on 
the  water  by  the  piston  P. 

This  important  property  may  be  further  elucidated  as  fol- 
lows : — 

We  have  supposed  that  the  two  apertures  and  the  pistons 
which  fill  them  were  equal  in  magnitude.  Let  us  now  suppose 
that  the  aperture  O'  is  ten  iimes  the  magnitude  of  the  aperture 
O  (fig.  3.).  It  follows,  from  what  has  been  already  explained, 
that  a  pressure  of  one  pound  acting  inwards  at  P  will  produce  a 
pressure  of  one  pound  acting  outwards  on  every  square  inch  in 
the  base  of  the  piston  P' ;  and  therefore  the  piston  P'  will  be 
urged  upwards  by  a  force  amounting  to  ten  pounds.  Accord- 
ingly, we  shall  find  that  if  this  piston  be  loaded  with  a  weight 
of  ten- pounds,  it  will  resist  the  pressure  of  the  liquid,  and  will 
not  suffer  itself  to  be  forced  upwards  in  the  cylinder  ;  but,  on 
the  other  hand,  this  weight  will  not  enable  it  to  force  the  liquid 
inwards,  and  it  will  merely  maintain  its  position.  If  it  beload- 

i* 


6  A  TREATISE  ON  HYDROSTATICS.  CHAP.  II, 

Fig.  3. 


ed  with  a  weight  greater  than  ten  pounds,  it  will  force  the  liquid 
inwards,  and  will  raise  the  piston  P  ;  and  if  it  be  loaded  with  a 
weight  less  than  ten  pounds,  the  piston  P  will  force  it  upwards. 
It  appears,  therefore,  that  the  pressure  exerted  on  the  ten 
square  inches  of  surface  forming  the  base  of  the  piston  P;  is  ten 
pounds,  and  neither  more  nor  less.  In  the  same  manner,  what- 
ever be  the  proportion  which  the  base  of  the  greater  piston  P' 
bears  to  the  base  of  the  lesser  piston  P,  in  exactly  the  same 
degree  will  the  force  transmitted  by  the  liquid  from  P  to  P'  be 
multiplied. 

There  are  some  circumstances  which  impair  the  accuracy 
with  which  the  practical  results  of  the  experimental  illustrations, 
conducted  in  the  manner  just  described,  represent  the  conclu- 
sions at  which,  by  reasoning,  we  have  arrived.  That  the  pis- 
tons P,  P'  may  move  in  the  cylinders  so  as  not  to  allow  the 
liquid  to  escape  between  them  and  the  inner  surface  of  the  tube, 
it  is  necessary  that  they  should  press  upon  that  surface  with  a 
certain  force  ;  this  pressure  will  unavoidably  be  accompanied 
by  friction  ;  and,  before  the  pressure  excited  on  one  piston  can 
produce  a  perceptible  effect  in  moving  the  other,  an  excess  of 
force  must  be  produced  sufficient  to  overcome  the  friction  of 
both  pistons.  Thus,  m  Jig.  2.,  if  the  pistons  be  equally  loaded, 
a  small  additional  weight  on  either  will  not  always  cause  the 
other  to  ascend ;  it  will  only  do  so  when  its  force  exceeds  the 
amount  of  the  resistance  occasioned  by  the  friction  of  the 
pistons. 

This  inconvenience  may  be  removed  by  applying  the  pressure 
on  the  surface  of  the  liquid  at  O  and  O'  by  some  means  which 
will  not  be  attended  with  perceptible  friction.  Such  means  are 
easily  found ;  and  although  they  may  at  the  first  view  appear  to 
confirm  the  theory  by  a  more  indirect  process,  yet,  when  duly 
considered,  it  will  be  perceived  that  the  method  is  not  only  di- 
rect, but  more  satisfactory  than  the  former. 

(4.)  Let  us  suppose  the  pistons  P,  P'  removed  from  the  cyl- 
inders, and  let  circular  plates,  so  formed  that  they  shall  exactly 


CHAP.  II.  EXPERIMENTAL  PROOF. 


cover  the  apertures  O,  O,  turn  upon  rods  which  extend  across 
the  holes,  so  that,  being  turned  upon  these  rods,  they  will  in 
one  position  completely  stop  the  apertures,  their  flat  faces  being 
presented  to  the  liquid,  as  in  Jig.  4. ;  while  in  another  position 
they  will  leave  the  apertures  open,  having  their  edges  turned 
towards  the  liquid,  as  in  Jig.  5.  Thus,  in  the  position  repre- 
sented in  Jig.  4.,  all  communication  between  the  liquid  in  the 
vessel  and  the  external  part  of  the  cylinder  is  cut  off,  while  in 
the  position  represented  in  Jig.  5.  there  is  a  free  communica- 
tion, i 
First,  let  the  two  valves  V,  V,  be  closed,  as  in  Jig.  4.,  and  let 
one  pound  of  oil  be  poured  into  the  cylinder  C.  It  is  evident 
that  the  valve  V  will  now  sustain  a  pressure  of  one  pound ;  and 
if  that  valve  were  removed,  as  the  oil  would  not  mix  with  the 
water,  but  rest  upon  it,  the  water  would  sustain  the  same  pres- 
sure. Let  the  valve  V  be  turned  till  it  assumes  the  position 
represented  in  Jig.  5. :  the  weight  of  the  oil  will  now  press  upon  - 
the  surface  of  the  water ;  and,  as  there  will  be  no  sensible  fric- 
tion between  the  oil,  and  the  surface  of  the  cylinder,  an  undi- 
minished  pressure  of  one  pound  will  be  transmitted  to  every 
square  inch  of  the  surface  of  the  vessel,  and,  among  others,  to 
the  surface  of  the  valve  V',  which  will  be  pressed  upwards  with 
a  force  of  that  amount.  That  the  valve  V  is  pressed  by  such  a 
force  may  be  made  manifest  as  follows : — Let  a  pound  of  oil  be 
poured  into  the  tube  C' :  this  will  press  upon  the  valve  V7  with 
a  force  of  one  pound ;  and  if  the  valve  V'  be  turned  into  the 
position  represented  in  Jig.  5.,  the  same  pressure  will  act  upon 
the  surface  of  the  water  below.  It  will  then  be  observed  that 
this  surface  will  maintain  its  position,  neither  forcing  the  oil 
up,  nor  being  forced  down  by  it.  If  less  than  a  pound  of  oil 
had  been  poured  into  the  tube  C',  the  pressure  of  the  water  be- 
low Avould  prevail,  and  its  surface  would  rise  in  the  tube  ;  and 
it  would  only  be  restored  to  its  former  position  by  pouring  in 
so  much  more  oil  as  would  make  the  weight  of  the  whole  one 
pound.  If  still  more  were  poured  in,  the  pressure  of  the  oil 
would  prevail,  and  the  surface  of  the  water  would  sink  in  the 


A  TREATISE  OX  HYDROSTATICS. 


CHAP.  ii. 


tube.     Thus  it  appears  conclusively,  that  a  pressure  of  one 
pound  exerted  at  V  is  transmitted  undiminished  to  V  ;  and  in 


:a 


£>  C 

the  same  way  is  transmitted  to  every  square  inch  on  the  surface 
of  the  vessel. 

(5.)  By  the  same  reasoning  it  may  be  shown,  that  if  the  cylinder 
C;  were  greater  than  C,it  would  require  a  proportionally  great- 
er weight  of  oil  to  resist  the  ascent  of  the  water,  and  we  should 
arrive  at  the  same  conclusions  as  we  have  obtained  respecting 
the  piston  represented  in  Jig.  3. 

(o.)  By  this  singular  power  of  transmitting  pressure,  a  fiuid 
becomes,  in  the  strictest  sense  of  the  term,  a  machine,  and  one 
of  unequalled  simplicity  and  almost  unlimited  power:  as  such, 
it  is  amenable  to  ail  the  laws,  and  fulfils  all  the  conditions,  to 
which  ordinary  machines  are  subject.  The  surprising  effects 
which  are  consequent  on  the  property  of  liquids  which  we  have 
just  explained,  exhibited  under  various  forms,  which  we  shall 
presently  have  occasion  to  notice  more  particularly,  have  ac- 
quired for  it  the  name  of  the  ."  hydrostatic  paradox."  But,  in 
truth,  there  is  nothing  in  these  effects  more  deserving  the  title 
of  paradox  than  those  which  attend  every  machine.  In  various 
parts  of  our  treatise  on  Mechanics,  and  more  especially  in  the 
twelfth  chapter  of  that  volume,  it  has  been  proved  that  there  is 
nothing  paradoxical,  or  repugnant  to  the  results  of  common  ob- 
servation, in  the  effects  produced  by  machinery.  We  shall  now 
endeavor  to  show  that  the  same  principles  arc  applicable,  and 
the  same  explanations  satisfactory,  when  a  liquid  is  used  as  a 
machine  ;  that  is,  as  a  means  of  transmitting  fcrce  from  one 
point  to  another. 

A  force  of  a  pound  acting  on  the  piston  P.fg.  6.,  holds  in 
equilibrium  a  force  of  ten  pounds  acting  on  the  piston  P;.  In 
this  case,  however,  it  must  not  be  supposed  that  the  piston  P 
supports  the  ten  pounds  which  press  down  tiio  piston  P7 :  the 
bottom  of  the  vessel  sustains  by  its  resistance  nine  of  the  ten 
pounds  acting  on  the  piston  P;,  and  the  remaining  pound  alone 
is  resisted  by  the  piston  P. 

The  circumstances  attending  the  action  of  these  forces  differ 


CHAP.    II.  A    LIQUID    IS    A    MACHINE. 


in  nothing  from  those  of  a  lever  of  the  first  kind,  supporting  a 
weight  of  ten  pounds  on  the  shorter  arm,  balanced  by  a  weight 
of  one  pound  on  the  longer  arm.  The  liquid  performs  the  office 
of  the  bar,  by  transmitting  the  effect  of  the  lesser  weight  to  the 
greater ;  and  the  surfaces  of  the  vessel  which  contains  the 
liquid  perform  the  office  of  the  fulcrum,  by  sustaining  both  the 
power  and  weight.* 

If  the  piston  P  be  used  to  raise  the  piston  P',  instead  of 
merely  supporting  it,  what  has  been  regarded  as  paradoxical 
in  the  process  may  likewise  be  explained  almost  in  the  same 
words  which  have  been  used  in  explaining  several  machines  in 
our  treatise  on  Mechanics.  If  the  piston  P  be  made  to  descend 
one  inch,  a  quantity  of  water  which  occupies  one  inch  of  the 
cylinder  C  will  be  expelled  from  it ;  and  as  the  vessel  A  B  C  D 
is  filled  in  every  part,  and  its  sides  cannot  yield,  the  piston  P' 
must  be  forced  up  until  room  be  obtained  for  the  water  which 
has  been  expelled  from  C.  But  as  the  cylinder  C'  is  ten  times 
larger  than  the  cylinder  C,  the  height  through  which  the  piston 
P'  must  be  moved  to  obtain  this  room  will  be  ten  times  less 
than  that  through  which  the  piston  P  was  caused  to  descend. 
Thus,  while  one  pound  on  the  piston  P  was  moved  through  one 
inch,  a  weight  of  ten  pounds  on  the  piston  P7  has  been  moved 
through  the  tenth  of  an  inch.  By  repeating  this  process  ten 
times,  we  shall  move  ten  pounds  on  the  piston  P'  through  a 
height  of  one  inch,  by  ten  distinct  efforts,  each  of  which  moves 
one  pound  through  one  inch.  The  force  expended,  and  the 
effect  produced,  is  therefore  the  same  as  if  the  weight  of  ten 
pounds,  with  which  the  piston  Pf  was  loaded,  were  divided  into 
ten  equal  parts,  and  these  parts  severally  raised  by  ten  distinct 
efforts  through  the  height  of  an  inch.  The  force,  therefore^ 
expended  to  produce  a  given  effect  is  the  same  as  if  no  ma- 
chine was  used.f 

<7.)  It  is  not  the  least  surprising  circumstance  in  the  history 

*  Mechanics,  (311.)  t  U>id.  (2260 


10  A    TREATISE    ON   HYDROSTATICS.          CHAP.    II. 

of  physical  science,  that  this  property  of  liquids,  though  long 
known,  and,  indeed,  the  subject  of  curious  observation,  should 
have  continued,  until  a  comparatively  recent  period,  a  barren 
fact.  The  engine  known  by  the  name  of  the  HYDROSTATIC  or 
HYDRAULIC  PRESS,  and  sometimes,  from  the  name  of  the  engi- 
neer who  gave  it  its  present  form,  and  brought  it  into  general 
use,  BRAMAH'S  PRESS,  is  nothing  more  than  a  simple  and  direct 
practical  application  of  the  property  which  we  have  just  in- 
vestigated. 

A  small  cylinder,  C,Jlg.  7..  is  furnished  with  a  piston  or  plug, 
A,  which  moves,  water  tight,  in  it ;  at  the  bottom  of  this  cylin- 
der there  is  a  valve,  B,  which  opens  upwards  and  communicates 
with  a  tube  below,  which  descends  into  a  vessel  or  reservoir  of 
\vater.  In  the  side  of  the  cylinder  C  there  is  a  narrow  tube, 
D,  inserted  in  the  cylinder,  and  communicating  at  E  with  an- 
other cylinder,  C',  of  much  greater  dimensions.  In  this  cylin- 
der there  is  a  large  piston,  A',  the  rod  of  which  is  directed 
against  whatever  object  the  machine  is  intended  to  sustain  or 
move.  We  shall  at  present  suppose  it  applied  to  an  ordinary 
press :  G  H  I K  represents  a  strong  iron  frame,  and  F  a  square 
plate  movable  in  it  and  resting  on  the  piston  rod.  As  the  pis- 
ton rod  is  moved  up,  the  plate  F  is  forced  up  towards  the  top 
of  the  press  H  I,  so  that  any  substance  placed  between  the 
plate  F  and  the  top  H  I  is  submitted  to  pressure.  In  the  tube 
D  E  there  is  a  valve,  O,  which  opens  towards  the  great  cylinder 
C' ;  and  in  the  same  tube  there  is  a  stop-cock,  P,  by  which  a 
communication  with  the  cistern  below  may  bo  opened  and 
closed  at  pleasure. 

The  rod  of  the  small  piston  A  is  connected  at  X  with  a  lever, 
L  M,  which  plays  upon  a  fulcrum  at  M.  The  press  is  worked 
by  raisjng  and  depressing  alternately  the  lever  at  L,  and  the 
process  is  effected  as  we  shall  now  describe. 

Suppose  the  water,  if  there  be  any  in  the  cylinder  C',  is  dis- 
charged into  the  reservoir  by  the  cock  P,  which  is  then  closed  ; 
the  piston  A7  will  then  fall  to  the  bottom  of  the  cylinder.  Let 
us  also  suppose  that  the  piston  A  is  at  the  bottom  of  the  cylin- 
der C.  If  the  lever  L  be  nor/  raised,  the  piston  A  will  be  ele- 
vated, and  the  space  below  it  in  the  cylinder,  being  free  from 
air,  the  atmospheric  pressure*  will  force  the  water  in  the  reser- 
voir up  through  the  valve  B  so  as  to  lill  the  cylinder  C  :  this 
water  cannot  return  through  the  valve  B,  since  that  valve  opens 
upwards,  and  the  weight  of  the  water  above  it  only  keeps  it 
more  firmly  closed.  Let  the  lever  L  be  now  depressed :  the 
water  below  the  piston  A  will  be  forced  through  the  valve  O, 
and  through  the  tube  D  E,  into  the  great  cylinder  C'.  Let  this 

*  This  effect  v.-ill  be  explained  in  Pneumatics. 


CHAP.    II. 


THE    HYDROSTATIC    PRESS. 


11 


process  be  continued  until  the  space  in  the  great  cylinder  below 
the  piston  is  completely  filled  Avith  water :  when  that  is  accom- 
plished, the  pressure  of  the  piston  A  will  be  transmitted  to  the 
piston  A',  multiplied  in  the  proportion  of  the  magnitude  of  the 
piston  A.'  to  that  of  the  piston  A  (3.).  Thus,  if  the  magnitude 
of  the  piston  A'  be  a  thousand  times  that  of  A,  a  pressure  of 
ten  pounds  on  the  piston  A  will  produce  a  pressure  of  ten 
thousand  pounds  on  the  piston  A'.  During  the  operation  of 
the  machine,  at  the  intervals  of  the  ascent  of  the  piston  A,  it3 


Fig.  7. 


action  on  piston  A'  is  suspended ;  and  if  the  tube  of  communi- 
cation D  E  were  open,  the  piston  A'  would  press  upon  the  valve 
B  during  every  ascent  of  the  piston  A,  and  would  resist  the 
entrance  of  water  into  the  small  cylinder,  and  thus  the  operation 
of  the  machine  would  he  obstructed  :  but  the  valve  O,  opening 


10  A   TREATISE    ON    HYDROSTATICS.          CHAP.    II. 

of  physical  science,  that  this  property  of  liquids,  though  long 
known,  and,  indeed,  the  subject  of  curious  observation,  should 
have  continued,  until  a  comparatively  recent  period,  a  barren 
fact.  The  engine  known  by  the  name  of  the  HYDROSTATIC  or 
HYDRAULIC  PRESS,  and  sometimes,  from  the  name  of  the  engi- 
neer who  gave  it  its  present  form,  and  brought  it  into  general 
use,  BRAMAH'S  PRESS,  is  nothing  more  than  a  simple  and  direct 
practical  application  of  the  property  which  we  have  just  in- 
vestigated. 

A  small  cylinder,  C,fig.  7.,  is  furnished  with  a  piston  or  plug, 
A,  which  moves,  water  tight,  in  it ;  at  the  bottom  of  this  cylin- 
der there  is  a  valve,  B,  which  opens  upwards  and  communicates 
with  a  tube  below,  which  descends  into  a  vessel  or  reservoir  of 
water.  In  the  side  of  the  cylinder  C  there  is  a  harrow  tube, 
D,  inserted  in  the  cylinder,  and  communicating  at  E  with  an- 
other cylinder,  C;,  of  much  greater  dimensions.  In  this  cylin- 
der there  is  a  large  piston,  A',  the  rod  of  which  is  directed 
against  whatever  object  the  machine  is  intended  to  sustain  or 
move.  We  shall  at  present  suppose  it  applied  to  an  ordinary 
press :  G  H  I K  represents  a  strong  iron  frame,  and  F  a  square 
plate  movable  in  it  and  resting  on  the  piston  rod.  As  the  pis- 
ton rod  is  moved  up,  the  plate  F  is  forced  up  towards  the  top 
of  the  press  H  I,  so  that  any  substance  placed  between  the 
plate  F  and  the  top  H  I  is  submitted  to  pressure.  In  the  tube 
D  E  there  is  a  valve,  O,  which  opens  towards  the  great  cylinder 
C' ;  and  in  the  same  tube  there  is  a  stop-cock,  P,  by  which  a 
communication  with  the  cistern  below  may  be  opened  and 
closed  at  pleasure. 

The  rod  of  the  small  piston  A  is  connected  at  X  with  a  lever, 
L  M,  which  plays  upon  a  fulcrum  at  M.  The  press  is  worked 
by  raisjng  and  depressing  alternately  the  lever  at  L,  and  the 
process  is  effected  as  we  shall  now  describe. 

Suppose  the  water,  if  there  be  any  in  the  cylinder  C',  is  dis- 
charged into  the  reservoir  by  the  cock  P,  which  is  then  closed  ; 
the  piston  A'  will  then  fall  to  the  bottom  of  the  cylinder.  Let 
us  also  suppose  that  the  piston  A  is  at  the  bottom  of  the  cylin- 
der C.  If  the  lever  L  be  now  raised,  the  piston  A  will  be  ele- 
vated, and  the  space  below  it  in  the  cylinder,  being  free  from 
air,  the  atmospheric  pressure*  will  force  the  water  in  the  reser- 
voir up  through  the  valve  B  so  as  to  ii!l  the  cylinder  C  :  this 
water  cannot  return  through  the  valve  B,  since  that  valve  opens 
upwards,  and  the  weight  of  the  water  above  it  only  keeps  it 
more  firmly  closed.  Let  the  lever  L  be  now  depressed :  the 
water  below  the  piston  A  will  be  forced  through  the 'valve  O, 
and  through  the  tube  D  E,  into  the  great  cylinder  C'.  Let  this 

*  This  effect  v.-ill  be  explained  in  Pneumatics. 


CHAP.    II. 


THE    HYDROSTATIC    PRESS. 


11 


process  be  continued  until  the  space  in  the  great  cylinder  below 
the  piston  is  completely  filled  with  water :  when  that  is  accom- 
plished, the  pressure  of  the  piston  A  will  be  transmitted  to  the 
piston  A',  multiplied  in  the  proportion  of  the  magnitude  of  the 
piston  A'  to  that  of  the  piston  A  (3.).  Thus,  if  the  magnitude 
of  the  piston  A'  be  a  thousand  times  that  of  A,  a  pressure  of 
ten  pounds  on  the  piston  A  will  produce  a  pressure  of  ten 
thousand  pounds  on  the  piston  A'.  During  the  operation  of 
the  machine,  at  the  intervals  of  the  ascent  of  the  piston  A,  it3 


Fig.  7. 


action  on  piston  A'  is  suspended ;  and  if  the  tube  of  communi- 
cation D  E  were  open,  the  piston  A'  would  press  upon  the  valve 
B  during  every  ascent  of  the  piston  A,  and  would  resist  the 
entrance  of  water  into  the  small  cylinder,  and  thus  the  operation 
of  the  machine  would  be  obstructed  :  but  the  valve  O,  opening 


14  A  TREATISE  ON  HYDROSTATICS.  CHAP.  II. 

Fig.  7. 


the  action  of  the  hydrostatic  press.  If  the  funnel  be  removed, 
and  six  men  stand  on  the  board  B  C,  one  of  them,  blowing 
into  the  tube  T  with  his  mouth,  may  produce  a  sufficient  pres- 
sure on  the  column  of  water,  to  raise  the  board  and  its  load. 

(9.)  If  a.  long  narrow  tube  A,  Jig.  8.,  be  inserted 
perpendicularly  into  a  vessel  B,  filled  with  water, 
the  weight  of  a  few  ounces  of  water  may  be  so  ap- 
plied as  to  burst  the  vessel,  whatever  be  its  strength, 
provided  the  tube  be  sufficiently  long  and  narrow. 
This  will  be  easily  understood  upon  the  principles 
already  explained.  Let  us  suppose  that  the  magni- 
tude of  the  bore  of  the  tube  is  the  hundredth  part 
of  a  square  inch,  and  that  it  ascends  perpendicular- 
ly, to  such  a  height  above  the  vessel  that  it  may 
contain  an  ounce  of  water,  that  part  of  the  water  in 
the  vessel  which  is  immediately  under  the  mouth  of 
the  tube  will  receive  a  pressure  of  one  ounce  from 
the  incumbent  column.  The  magnitude  of  the  mouth  of  the  tube 
being  the  hundredth  of  a  square  inch,  it  follows,  from  what  has 
been  already  proved,  that  every  hundredth  part  of  a  square  inch 
in  the  surface  of  the  vessel  will  sustain  a  pressure  of  one  ounce, 
and  therefore  every  square  inch  will  sustain  a  pressure  of  100 
ounces.  A  square  foot  contains  144  square  inches,  and  there- 
fore every  square  foot  will  sustain  a  pressure  of  14,400  ounces 


CHAP.  II.  HYDROSTATIC  PARADOX.  15 

or  900  pounds.  Hence,  if  the  base  of  the  vessel  measure  nine 
square  feet,  and  its  sides  thirty-six  square  feet,  and  its  top  nine 
square  feet,  we  shall  have  a  total  surface  of  54  square  feet,  each 
square  foot  bearing  a  pressure  of  900  pounds,  and  the  whole 
surface  sustaining  a  pressure,  tending  to  burst  the  vessel, 
amounting  to  more  than  twenty-one  tons,  and  this  enormous 
force  is  produced  by  the  mechanical  modification  which  the 
weight  of  one  ounce  of  water  undergoes. 

(10.)  The  property  of  liquids,  which  has  been  under  consid- 
eration, points  them  out  as  an  easy,  simple,  and  effectual  means 
of  transmitting  force  to  any  distance,  and  under  circumstances 
in  which  other  mechanical  contrivances  would  be  totally  inap- 
plicable. It  is  only  necessary  to  carry  a  tube  filled  with  a  liquid 
from  the  point  where  the  force  originates,  to  the  point  to  which 
it  is  to  be  transmitted  ;  and  as  the  shape  or  position  of  the  con- 
necting tube  or  pipe  does  not  affect  the  property  of  the  fluid 
which  it  contains,  there  is  scarcely  any  conceivable  impediment 
which  can  prevent  the  transmission  of  the  force  from  the  one 
point  to  the  other.  A  pressure  excited  on  the  liquid  at  one  end 
of  the  tube,  will  be  communicated  to  any  surface  in  contact 
with  the  liquid  at  the  other  end,  whether  the  tube  between  the 
two  extremities  be  straight,  curved,  or  angular,  or  whether  it 
pass  upwards,  downwards,  or  in  an  oblique  or  horizontal  direc- 
tion. It  may  be  carried  through  the  walls  of  a  building,  through 
the  course  of  a  river,  under,  over,  or  around  any  obstruction  or 
impediment,  or,  in  fact,  according  to  any  course  or  direction 
whatsoever.  If  a  tube  filled  with  water  extended  from  London 
to  York,  a  pressure  excited  on  the  liquid  at  the  extremity  in 
London,  would  be  instantaneously  transmitted  to  the  extremity 
at  York.  It  has  been  suggested,  that  such  means  might  be 
used  for  telegraphic  communications,  in  situations  where  the 
frequency  or  importance  would  justify  the  expense  of  laying 
down  pipes  or  tubes.  An  ingenious  person  in  this  country  has 
tried  the  experiment  with  this  view,  and  has  laid  down  several 
miles  of  pipe  for  the  purpose.  Such  a  method  of  communica- 
tion would  have  the  advantage  of  being  independent  of  those 
accidental  interruptions  to  which  lights,  signals,  and  other  simi- 
lar contrivances  are  exposed. 

(11.)  The  power  of  liquids  to  transmit  pressure  has  been  pro- 
posed to  be  applied  to  surgical  purposes  by  Dr.  Arnott.  It 
would  indeed  seem  to  be  peculiarly  applicable  in  cases 'where 
it  is  necessary  to  produce  a  pressure  on  some  internal  part, 
which  cannot  be  approached  except  by  a  tube  or  channel, 
through  which  an  instrument  cannot  be  safely  or  conveniently 
inserted.  Dr.  Arnott  considers  that  a  liquid  might  be  conveyed 
through  a  flexible  tube,  so  shaped,  that  when  filled  by  the  liquid, 
the  proper  degree  of  pressure  will  be  excited  on  those  parts 


16  A  TREATISE  ON  HYDROSTATICS  CHAP.  II, 

which  require  it.     An  account  of  these  instruments  may  be  seen 
in  Dr.  Arnott's  work  on  Physics. 

(12.)  The  animal  economy  presents  innumerable  examples 
of  the  power  of  fluids  in  transmitting  pressure.  The  bones  and 
harder  parts  of  the  body  furnish  a  beautiful  example  of  a  struc- 
ture, in  which  every  leading  principle  of  mechanics,  commonly 
so  called,  is  illustrated.  The  fluids,  in  like  manner,  exhibit 
equally  apt  illustrations  of  the  principles  of  hydrostatics.  The 
heart,  the  fountain  from  which  the  blood  is  supplied  to  all  parts 
of  the  system,  is  an  instrument  possessing  great  power  of  ex- 
pansion and  contraction :  by  exciting  a  pressure  upon  the  blood, 
it  impels  that  fluid  into  the  arteries,  pressing  forward  what  has 
already  filled  them  through  proper  channels  of  communication 
into  the  veins.  These  various  pipes  and  conduits  are  formed 
of  an  elastic  material,  capable  of  continuing  the  pressure  com- 
menced at  the  heart,  and  thus  urging  forward  the  stream  of  li- 
quid, until  its  circulation  is  completed. 

As  in  the  pipe  D  £,/#.  6.,  of  the  hydrostatic  press,  valves  are 
provided  in  proper  places  in  the  various  tubes  through  which 
the  circulation  is  carried  on.  These  valves  are  so  contrived, 
that  the  blood  is  admitted  to  pass  freely  in  obedience  to  the 
impulse  it  receives  from  the  muscular  pressure ;  but  when  that 
pressure  is  intermitted,  the  fluid  cannot  return,  and  the  resist- 
ance of  the  closed  valve  supplies  the  place  of  the  moving  power 
whose  action  is  suspended.  < 

The  muscular  power  of  the  heart  to  excite  a  pressure  on  the 
blood  is  placed  in  a  very  striking  point  of  view,  by  an  experi- 
ment recorded  in  a  work  by  Dr.  Hales,  called  Statical  Essays. 
A  perpendicular  tube  is  made  to  communicate  with  the  blood 
of  one  of  the  arteries  of  an  animal.  The  blood  being1  no  longer 
confined,  rushes  into  the  tube,  and  ascends  to  a  height  above 
the  level  of  the  heart,  which  is  proportionate  to  the  pressure 
which  it  receives.  This  height  necessarily  varies  in  different 
animals ;  in  the  larger  and  more  powerful  species,  it  is  much 
greater  than  in  the  smaller  ones.  In  the  case  of  a  horse,  the 
column  will  ascend  to  about  ten  feet  above  the  heart.  The 
pressure  to  which  it  is  subject  in  the  veins  is  much  less  than  in 
the  arteries.  Dr.  Hales  found  that,  in  the  human  body,  the 
pressure  of  the  arterial  blood  was  capable  of  sustaining  a  co- 
lumn eight  feet  in  height,  and  amounted  to  four  pounds  on  the 
square  inch ;  while  the  pressure  of  the  venous  blood  did  not 
exceed  a  quarter  of  a  pound  on  the  inch,  and  only  sustained  a 
column  six  inches  in  height. 


CHAP.    III.  PRESSURE    FROM    WEIGHT.  17 


CHAP.    III. 
OF  THE  PRESSURE  PRODUCED  BY  THE  WEIGHT  OF  A  LIQUID. 

PRESSURE  PROPORTIONAL  TO  THE  DEPTH. — PRESSURE  ON  THE  HOR1 
ZONTAL  BOTTOM  AND  PERPENDICULAR  SIDES  OF  A  VESSEL. — EX 
PERIMENTAL  PROOFS  OF  THE  PROPERTY. — TOTAL  PRESSURE  ON 
THE  PERPENDICULAR  SIDE  OF  A  VESSEL  COMPUTED. — EMBANK- 
MENTS, DAMS,  AND  FLOODGATES. — METHOD  OF  COMPUTING  THE 
TOTAL  PRESSURE  ON  THE  SURFACE  OF  A  VESSEL  OF  ANY  SHAPE. 
— EXAMPLES. — GLOBE.— CUBE.— VARIOUS  EFFECTS  PRODUCED  BY 
THE  PRESSURE  OF  LIQUIDS  AT  GREAT  DEPTHS. — CORK  FORCED 
INTO  A  BOTTLE. — WATER  FORCED  I'NTO  THE  PORES  OF  WOOD. — 
LIQUIDS  NOT  ABSOLUTELY  INCOMPRESSIBLE. — EXPERIMENT  TO 
PROVE  THIS. 

(13.)  IN  the  investigation  contained  in  the  last  chapter,  the 
effects  of  the  weight  of  the  liquid  itself  were  left  out  of  con- 
sideration, and  it  was  merely  regarded  as  a  machine  by  which 
other  forces  might  be  transmitted  and  modified.  In  the  same 
manner,  however,  and  upon  the  same  principles,  as  it  transmits 
and  modifies  other  forces,  it  conveys  the  effect  of  its  own 
weight  through  the  dimensions  which  it  occupies  in  the  vessel 
which  contains  it.  This  weight  exerts  a  certain  pressure  on 
every  part  of  the  surface  of  the  containing  vessel  with  which  it 
is  in  contact.  The  total  amount  of  this  pressure,  as  well  as  the 
portion  of  it  which  each  part  of  the  surface  sustains,  is  to  be 
inferred  from  a  consideration  of  the  weight  of  the  liquid,  its 
power  of  transmitting  pressure,  and  the  peculiar  figure  or  shape 
of  the  vessel.  It  may,  however,  here  be  observed,  generally, 
that  the  effect  is  totally  .different  from  that  which  would  be 
produced  by  a  solid. 

(14.)  There  is  one  general  principle  by  which  the  pressure 
of  a  liquid  on  the  surface  of  the  vessel  which  contains  it  may 
always  be  ascertained.  Each  part  of  the  surface  of  the  vessel, 
in  contact  with  the  liquid,  sustains  a  pressure  equal  to  the 
weight  of  a  column  of  the  liquid,  whose  height  is  equivalent  to 
the  depth  of  the  part  of  the  surface  of  the  vessel  in  question 
below  the  surface  of  the  liquid  contained  in  the  vessel.  The 
truth  of  this  general  principle  will  be  apparent,  by  considering 
it,  first,  in  the  more  simple  and  obvious  cases,  and  tracing  it 
thence  to  the  more  complex  and  difficult  ones. 

Let  ABC,  Jig.  9.,  be  a  long  square  pipe  in  a  perpendicular 
position,  each  of  whose  sides  is  an  inch  broad.  The  base  B  C, 
therefore,  is  a  square,  each  of  whose  sides  is  an  inch.  Suppose 
this  base  to  be  closed  by  a  flat  bottom,  and  let  water  be  poured 


A    TREATISE    ON    HYDROSTATICS.          CHAP.    III. 

Fig.  9.  into  the  pipe  until  it  attain  an  elevation  B'C'  one  inch 
above  the  bottom  of  the  pipe.  The  liquid  will  now 
}A  be  in  contact  with  a  square  inch  of  surface  on  each 
of  the  four  sides,  besides  the  square  inch  of  surface 
which  forms  the  bottom.  Let  a  flat  plate,  cut  into 
the  shape  of  a  square  inch  so  as  to  fit  the  tube,  be 
now  conceived  to  be  introduced  into  it,  and  placed 
immediately  on  the  surface  of  the  water,  and  in  con- 
tact  with  it.  If  any  weight,  as  10  pounds,  be  placed 
upon  this  plate,  the  liquid  below  will  transmit  a  pres- 
sure of  ten  pounds  to  every  square  inch  of  the  pipe 
with  which  the  water  is  in  contact,  and  therefore 
the  bottom,  and  each  of  the  four  sides,  will  several- 
•"  ly  sustain  a  pressure  of  ten  pounds.*  This  is  obvi- 
ous from  what  has  been  so  fully  explained  in  the 
last  chapter. 

If  the  plate  and  the  weight  with  which  it,  is  supposed  to  be 
pressed  be  removed,  and  ten  pounds  of  water  be  poured  into 
the  pipe,  the  water  below  the  level  B'C'  will  suffer  exactly  the 
same  mechanical  pressure  as  was  before  exerted  by  the  plate 
loaded  with  the  weight,  and  this  pressure  will  be  transmitted 
in  the  same  way  to  the  surface  of  the  tube,  by  the  Avater  below 
B'C'.  It  thus  appears  that  a  perpendicular  column  of  water, 
weighing  ten  pounds,  standing  above  the  level  B'C',  will  press, 
not  only  on  the  bottom  of  the  vessel,  but  on  the  sides  immedi- 
ately below  B'C',  with  a  force  amounting  to  ten  pounds. 

What  has  been  proved  of  the  column  of  fluid,  above  the  level 
B'C',  will  be  equally  true  of  any  other  part  of  the  column  of 
fluid  contained  in  the  tube.  Thus  the  column  of  fluid  above 
the  level  B"C",  will  communicate  a  pressure  to  every  square 
inch  of  the  surface  of  the  vessel  below  that  level,  amounting 
to  its  own  weight. 

To  render  the  explanation  more  clear  and  simple,  the  section 
of  the  pipe  has  been  here  supposed  to  be  square,  and  its  magni- 
tude to  be  one  inch ;  but  a  little  attention  and  consideration 
will  show,  that  the  same  reasoning,  with  slight  changes,  will 
be  applicable,  whatever  be  the  magnitude  of  the  vessel,  and 
whatever  be  the  shape  of  its  base.  If  any  part  of  the  column 
is  supposed  to  be  removed,  and  a  flat  plate  fitting  the  vessel, 
and  loaded  with  a  weight  equal  to  that  of  the  water  removed,  be 
introduced,  the  force  of  thit  weight  will  be  transmitted  by  the 
water  below,  with  undiminished  energy,  to  every  part  of  the 
surface  of  the  vessel  with  which  it  is  in  contact.  Each  portion 
of  the  surface  of  the  vessel,  which  is  equal  in  magnitude  to  the 
surface  of  the  plate,  will  sustain  a  pressure  equal  to  the  force 

*  They  will  severally  sustain  n  pressure  of  ten  pounds  in  addition  to  the  pres- 
sure resulting  from  the  weight  of  the  fluid  itself.— AM.  ED. 


CHAP.  III.   PRESSURE  PROPORTIONAL  TO  DEPTH.        19 

with  which  the  plate  presses  on  the  water.  When  the  plate  is 
removed,  and  replaced  by  an  equivalent  weight  of  water,  the 
same  effect  will  be  continued. 

(15.)  It  therefore  appears  generally,  that  in  every  vessel 
whose  sides  are  perpendicular,  and  whose  bottom  is  horizontal, 
whatever  be  its  shape  in  other  respects,  the  pressure  on  the 
bottom  will  be  equal  to  the  whole  weight  of  the  fluid  which  it 
contains,  while  the  pressure  on  each  square  inch  of  the  perpen- 
dicular sides  will  be  equal  to  the  weight  of  a  column  of  the 
liquid,  whose  base  is  a  square  inch,  and  whose  height  is  equal 
to  the  depth  of  the  part  of  the  surface  of  the  vessel  in  question 
below  the  upper  surface  of  the  liquid  in  the  vessel. 

(16.)  It  appears  from  what  has  been  stated,  that  not  only  the 
surface  of  the  vessel  which  contains  a  liquid,  but  likewise  every 
part  of  the  liquid  itself,  sustains  a  pressure  from  the  weight  of 
the  liquid  above  it,  and  this  pressure  is  regulated  by  the  same 
law.  If  any  portion  of  the  liquid  be  selected  at  any  given 
depth  below  the  surface,  that  portion  is  pressed  equally  in  every 
possible  direction  by  the  surrounding  fluid,  and  the  amount  of 
the  pressure  which  it  thus  sustains  is  the  weight  of  the  column 
of  fluid  perpendicularly  above  it.  This  may  be  easily  deduced 
from  considering  the  property  of  liquids  explained  in  the  last 
chapter.  It  is  evident  that  a  part  of  the  fluid,  taken  any  where 
within  its  dimensions,  sustains  a  downward  pressure  from  the 
weight  of  the  incumbent  column ;  but  it  transmits  this  pressure;, 
by  the  property  just  alluded  to,  in  every  direction  around  it; 
downwards,  laterally,  obliquely,  &c.  .Now  it  is  clear  that  it 
must  encounter  an  equal  pressure  in  all  these  directions ;  for 
if  it  did  not,  it  would  move  away  in  that  direction  in  which  its 
force  was  unresisted ;  but  as  no  such  motion  takes  place,  and 
as  the  particles  of  the  fluid  remain  at  rest,  it  follows  that  they 
are  maintained  in  these  places,  by  forces  pressing  them  equally 
Fi*  10.  on  every  side  and  from  every  possible  direction,  each 
of  which  is  equal  to  the  weight  of  the  perpendicular 
column  of  fluid  above  the  particle  so  pressed. 

(17.)  This  property  may  easily  be  reduced  to  experi- 
mental proof.  Let  A  B^/Fg*.  10.,  be  a  strong  metal  cyl- 
inder, having  a  metal  bottom  at  B,  but  open  at  A :  in  this 
let  a  spiral  spring  be  inserted,  bearing  a  circular  plate 
C,  which  moves  water-tight  within  the  cylinder,  so  that 
a  force  applied  to  the  plate  C  will  overcome  the  elas- 
ticity of  the  spring,  and  cause  the  plate  to  move  into  the 
cylinder  towards  B.  The  farther  the  plate  advances 
within  the  cylinder,  the  more  powerful  the  elastic  force 
of  the  spring  will  become,  and  the  greater  will  be  the 
force  necessary  to  prevent  its  recoil.  The  amount  of 
force  necessary  to  press  the  plate  to  any  proposed  depth 


j| 


20 


A    TREATISE    OX    HYDROSTATICS. 


CHAP.    HI. 


in  the  cylinder,  may  be  determined  by  experiment ;  and  it  is  not 
difficult  to  provide  a  means  of  registering  the  depth  within  the 
cylinder,  to  which  the  plate  may  have  been  forced  on  any  oc- 
casion, when  the  presence  of  an  observer  is  rendered  impossi- 
ble. If  such  an  instrument  be  plunged  in  a  liquid  to  any 
depth,  the  pressure  exerted  by  the  fluid  will  force  in  the 
movable  plate  ;  and,  upon  observing  the  instrument  when 
drawn  out,  the  amount  of  the  pressure  will  be  known  from 
the  space  through  which  the  plate  was  forced  into  the  cyl- 
inder. If  the  instrument  be  successively  immersed  to  depths 
of  1,  2,  and  3  yards,  it  will  be  found  that  the  pressures 
which  have  acted  on  the  spring,  are  in  the  proportions  of  the 
numbers  1, 2,  3,  and  are  equal  to  the  weights  of  columns  of  the 
liquid  whose  heights  are  respectively  equal  to  the  depths  of 
immersion,  and  whose  bases  are  equal  to  the  movable  plate. 
The  fact  that  the  pressure  is  proportional  to  the  depth,  and 
equal  to  the  weight  of  the  incumbent  column,  is  thus  conclu- 
sively established. 

That  this  pressure  is  exerted  equally  in  every  possible  direc- 
tion, may  be  shown  by  giving  the  instrument,  at  the  same  depth 
successively,  different  positions.  If  it  be  first  immersed  with 
the  end  A  presented  upwards,  and  the  distance  observed  through 
which  the  plate  is  forced  in,  and  then  successively  immersed 
to  the  same  depth  with  the  end  A  presented  downwards,  side- 
ways, and  in  any  other  direction,  it  will  always  be  observed 
that  the  distance  through  which  the  plate  is  forced  by  the  pres- 
sure of  the  liquid  will  be  the  same  ;  indicating  thereby,  that  the 
pressures  in  all  those  directions  are  equal. 

(18.)  This  important  law  may  be  established  experimentally 
by  a  more  easy  and  scarcely  less  direct  method.  Let  four 
glass  tubes,  T,Jig.  11.,  be  provided,  open  at  both  ends,  and  let 

Fig.  11. 


one  end  of  the  first  be  straight  ;  of  the  second,  turned  upwards  ; 
of  the  third,  turned  sideways  ;  and  of  the  fourth,  turned  in  an 
oblique  direction.  At  these  ends  let  stop-cocks  be  placed, 
which  may  be  opened  and  closed  at  pleasure.  These  cocks 


CHAP.  HI.   PRESSURE  PROPORTIONAL  TO  DEPTH.       21 

being  closed,  let  all  the  tubes  be  immersed  to  the  same  depth 
in  a  vessel  of  water.  The  water  Avill  then  press  against  each 
of  the  cocks  with  a  certain  force,  the  amount  of  which  it  is  re- 
quired to  ascertain.  We  shall  suppose  the  bores  of  the  tubes 
to  be  equal,  although  that  circumstance,  as  will  hereafter  ap- 
pear, cannot  affect  the  result  of  the  experiment.*  Let  us 
suppose  the  diameter  of  the  bores  of  each  of  the  tubes  to  be 
half  an  inch. 

The  water,  at  the  depth  to  which  the  tubes  are  immersed,  is 
in  this  case  acting  against  a  circular  surface,  of  the  diameter 
of  half  an  inch  at  each  stop-cock.  If  the  several  stop-cocks  be 
now  opened,  the  pressure  will  cause  the  water  to  rush  into  the 
tubes,  in  the  first  upwards,  in  the  second  downwards,  in  the 
third  sideways,  and  in  the  fourth  obliquely.  It  will  continue 
to  flow  into  each  until  the  weight  of  the  column,  which  has 
risen  in  the  tube,  is  sufficiently  great  to  resist  the  pressure  at 
its  extremity.  When  that  takes  place,  and  not  until  then,  the 
water  will  cease  to  flow  into  the  tube.  It  will  be  observed, 
that  in  each  tube  the  water  will  rise  until  it  has  attained  the 
level  of  the  water  in  the  vessel,  and  it  will  then  cease  to  flow 
It  follows,  therefore,  that  the  pressure  of  the  fluid  at  the  ex- 
tremity of  the  tubes  is  equal  to  the  weight  of  a  column  of  the 
fluid,  which  extends  perpendicularly  from  their  extremities  to 
the  surface  ;  and  since  the  water  will  always  rise  to  the  level 
of  the  fluid  in  the  vessel,  whatever  direction  may  be  given  to 
the  lower  extremity  by  bending  the  tube  near  that  point,  it  fol- 
lows, that  at  the  same  depth  the  pressure  in  every  possible 
direction  is  the  same. 

In  this  mode  of  illustration  it  will  easily  be  perceived,  that 
the  column  of  water  which  is  sustained  in  the  tube  performs  the 
part  of  the  stop-cock,  with  respect  to  the  water  which  presses 
in  at  the  orifice  below,  and  that  the  weight  of  this  column  ex- 
actly balances  this  pressure. 

There  will  be  no  difficulty  in  seeing  how  this  experiment 
may  be  generalized.  The  tubes  may  be  of  any  magnitudes, 
whether  equal  or  unequal,  and  still  the  water  will  rise  in  them 
to  the  level  of  the  water  in  the  vessel ;  and  the  same  will  hap- 
pen whatever  be  the  liquid  used.  The  pressure  exerted  at  any 
depth  below  the  surface  is  always  equal  to  the  weight  of  a 
column  of  the  liquid  whose  height  is  equal  to  the  depth,  and 
whose  base  is  equal  to  the  surface,  over  which  the  pressure  is 

*  When  the  boxes  of  the  tubes  are  unequal,  and  some  of  them  very  small,  ca- 
pillary action  will  sensibly  affect  the  result,  in  a  manner  depending  upon  the  na- 
ture of  the  fluid.  The  elevation  or  depression  of  the  fluid  in  the  smaller  tube, 
depends  upon  the  relation  which  subsists  between  the  action  of  the  tube  on  the 
fluid,  and  the  mutual  action  of  the  particles  of  the  fluid.  By  a  complete  analysis 
of  all  the  forces  concerned,  it  ?:i;i.y  be  shown  in  what  manner  their  opposite  effects 
may  be  produced. — As:.  11^. 


22  A    TREATISE    ON    HYDROSTATICS.  CHAP.  III. 

extended.  The  quantity  of  liquid  whose  weight  expresses  this 
pressure,  may  always  be  determined  arithmetically,  by  multi- 
plying the  number  of  inches  in  depth  below  the  surface  of  the 
liquid,  by  the  number  of  square  inches  in  the  surface  on  which 
the  pressure  is  exerted.  The  product  of  these  numbers  will 
be  the  number  of  solid  inches  of  the  liquid,  whose  weight  is 
equal  to  the  pressure.  It  must,  however,  be  understood,  that 
in  this  mode  of  calculation,  the  surface  pressed  is  supposed  to 
be  horizontal,  or  if  it  be  oblique,  its  dimensions  must  be  very 
small,  compared  with  the  depth. 

The  following  experiment  furnishes  another  illustration  of 
the  property  by  which  the  pressure  of  a  liquid  increases  with 
the  depth : — Let  a  bladder  be  attached  to  the  extremity  of  a 
glass  tube,  and  let  it  be  filled  with  mercury  to  a  small  height 
above  the  point  where  it  is  attached.  Let  equal  small  divisions 
be  marked  upon  the  tube,  beginning  from  the  surface  of  the 
mercury.  If  the  bladder  thus  filled  be  immersed  in  a  vessel  of 
water,  the  pressure  of  the  surrounding  liquid  will  cause  the 
mercury  to  ascend  in  the  tube.  Let  it  be  immersed  to  such  a 
depth  that  the  mercury  will  rise  through  one  division  of  the 
tube,  and  let  the  depth  of  immersion  be  observed  ;  let  the  tube 
be  then  immersed  to  twice  that  depth,  and  the  mercury  will  be 
observed  to  rise  through  another  division.  Being  immersed  to 
three  times  the  depth,  it  will  rise  to  a  third  division,  and  so  on. 
It  therefore  appears  that  the  pressure  upon  the  bladder  increases 
in  proportion  to  the  depth. 

(19.)  Concluding,  then,  that  every  part  of  a  liquid  suffers  and 
transmits  a  pressure,  arising  from  the  weight  of  the  incumbent 
liquid ;  that  this  pressure  is  always  proportional  to  the  depth, 
and  is  equally  exerted  in  every  direction ;  we  may  easily  obtain 
theorems  respecting  the  pressure  sustained  by  the  surface  of 
vessels  which  contain  liquids,  of  a  much  more  general  nature 
than  those  which  have  led  to  the  preceding  investigation. 

Whatever  be  the  shape  of  the  vessel  which  contains  a  liquid, 
each  square  inch  of  its  surface  suffers  a  pressure  equal  to  the 
weight  of  a  column  of  the  liquid,  whose  base  is  a  square  inch, 
and  whose  height  is  the  depth  of  that  part  of  the  surface  of  the 
vessel  below  the  surface  of  the  liquid.  This  follows  immedi- 
ately from  the  principle  which  has  just  been  established  ;  for  the 
liquid  which  is  in  immediate  contact  with  any  part  of  the  sur- 
face of  the  vessel,  sustains  a  pressure  in  a  direction  perpendic- 
ular to  that  surface,  to  the  amount  just  mentioned ;  and  it  is 
evident  that  the  surface  must  balance  and  resist  that  pressure. 

By  the  aid  of  the  peculiar  language  and  symbols  of  mathe- 
matical science,  general  rules  or  formularies  may  be  given,  by 
which  the  whole  pressure  of  a  liquid  on  the  surface  of  a  vessel 
of  any  proposed  figure  may  be  computed.  Although  great 


CHAP.  III.   PRESSURE  PROPORTIONAL  TO  DEPTH.        23 

practical  facility,  not  only  in  calculation,  but  also  in  reasoning-, 
may  be  derived  from  the  use  of  such  formulae,  yet  they  must  be 
understood  to  express  nothing  more  than  what  has  been  already 
explained.  The  method  by  which  they  express  it  is,  however, 
attended  with  great  convenience,  and  affords  considerable  ad- 
vantages in  the  application  of  the  general  principle  to  particular 
cases. 

(20.)  An  obvious  consequence  of  the  property  now  explained 
is,  that  the  pressure  produced  upon  the  surfaces  of  the  vessel 
containing  a  liquid,  can  never  in  any  case  be  less  than  the 
weight  of  the  liquid,  but  will  not  unfrequently  amount  to  many 
times  that  weight.  Since  the  general  methods  of  determining 
the  pressure  on  surfaces  do  not  admit  of  familiar  explanation, 
we  shall  endeavor  to  explain  the  principle  by  its  application  to 
such  particular  cases  as  can  be  rendered  intelligible  without 
mathematical  symbols. 

(21.)  If  the  surface  which  sustains  the  pressure  be  horizontal, 
every  part  of  it,  being  at  the  same  depth,  will  suffer  the  same 
pressure.  In  this  case,  therefore,  it  is  evident  that  the  total 
pressure  which  the  surface  sustains  is  the  weight  of  all  the 
liquid  which  is  perpendicularly  over  it,  or,  what  is  the  same,  the 
weight  of  a  column  of  the  liquid,  whose  base  is  equal  to  the 
surface,  and  whose  height  is  equal  to  the  depth. 

(22.)  If  the  surface  which  suffers  the  pressure  be  not  hori- 
zontal, its  several  parts  will  be  at  different  depths,  and,  there- 
fore, will  suffer  different  pressures.  If  a  point  could  be  found 
whose  depth  is  an  average  of  all  the  different  depths,  then  the 
total  pressure  would  be  the  same  as  if  the  whole  surface  were 
uniformly  subject  to  the  pressure  sustained  by  this-  point,  and 
the  total  amount  of  the  pressure  would  be  equal  to  the  weight 
of  a  column  of  the  liquid,  whose  base  is  equal  to  the  surface 
pressed,  and  whose  height  is  equal  to  the  depth  of  that  point. 
This  will,  perhaps,  be  more  clearly  comprehended  by  particular 
examples. 

Fig.  12. 


Let  A  B  C  D,  Jig.  12.,  be  a  vessel  with  a  flat  square  bottom 
and  perpendicular  sides  ;  and  suppose  it  filled  with  water  ;  and 
let  the  side  A  B  be  supposed  to  be  divided  into  ten  equal  parts, 
marked  by  the  numbers  1,  2,  3,  4,  to  10 :  the  pressure  at  the 


A  TREATISE  ON    HYDROSTATICS.  CHAP.  Ill, 

Fig.  12. 


8  0 

point  1  we  shall  suppose  to  be  one  pound.     The  point  2,  being- 
at  twice  that  depth,  will  sustain  a  pressure  of  two  pounds      The 
point  3  will  sustain  a  pressure  of  three  pounds,  and  SQ  on,  the 
lowest  point  sustaining  a  pressure  of  ten  pounds.     Since,  there- 
tore,  the  intensity  of  the  pressure  from  A  to  B  increases  uni- 
formly, the  point  which  sustains  the  average  pressure  will  be 
found  at  the  middle  of  the  depth  A  B.     This  point  is  that  which 
is  marked  5.     If  we  suppose  the  whole  surface  A  B  to  sustain 
the  same  pressure  as  that  which 'the  point  5  suffers,  the  total 
pressure  will  be  the  same  as  at  present.     A  very  slight  consid- 
eration of  the  effects  will  make  this  evident.     At  present  the 
point  0  sustains  a  pressure  of  six  pounds,  and  the  point  4  sus- 
tains a  pressure  of  four  pounds,  making  a  total  of  ten  pounds, 
these  two  points  each  sustained  a  pressure  of  five  pounds, 
which  is  the  average  pressure,  the  total  pressure  would  still  be 
the  same,  ten  pounds.     In  like  manner,  the  point  7  at  present 
sustains  a  pressure  of  seven  pounds,  and  the  point  3  a  pressure 
of  three  pounds,  which  together  make  ten  pounds.     If  each  of 
these  points  sustained  a  pressure  of  five  pounds,  the  sum  would 
be  the  same.     It  is  evident  that  the  same  reasoning  will  apply 
to  all  points  equally  distant  above  and  below  the  middle  point 
5.     The  pressure  on  each  point  below  it  exceeds  the  pressure 
at  5  by  exactly  as  much  as  the  pressure  on  a  point  equally  dis- 
tant above  it  falls  short  of  the  pressure  at  5.     Thus  the  excess 
and  defect  mutually  compensate  each  other,  and  a  general 
average  is  obtained. 

From  what  has  been  now  stated,  it  appears  that  the  total 
pressure  on  the  perpendicular  side  of  a  vessel  filled  with  a 
liquid,  is  the  same  as  if  that  side  were  converted  into  a  horizon- 
tal bottom,  and  half  the  depth  of  liquid  rested  on  it. 

It  also  appears  that  the  pressure  on  the  perpendicular  side  is 
entirely  independent  of  the  quantity  of  liquid  which  the  vessel 
contains.  The  perpendicular  sides  of  a  trough,  when  filled 
with  a  liquid,  will  sustain  the  same  pressure  whether  the  trough 
be  wide  or  narrow.  If  the  sides  be  separated  by  an  interval  of 
only  a  quarter  of  an  inch,  and  the  trough  contains  only  a  quart 
of  water,  the  pressure  on  the  sides  win  be  the  same  as  if  the 
sides  were  separated  many  yards,  and  the  trough  contained 
several  barrels  of  water. 


CHAP.  III. 


PRESSURE    ON    VESSELS.  25 


(23.)  If  the  sides  of  the  vessel  be  perpendicular,  and  the  bot- 
tom be  horizontal  and  flat,  the  pressure  on  the  sides  may  be 
estimated  in  the  same  manner  as  above,  whatever  be  the  shape 
of  the  bottom.  The  point  of  average  pressure  is,  in  this  case, 
always  at  half  the  entire  depth  below  the  surface  of  the  liquid  ; 
and  the  total  pressure  is  the  same  as  if  this  average  pressure 
were  uniformly  diffused  over  the  entire  surface  of  the  sides  in 
contact  with  the  liquid.  Thus,  if  the  vessel  be  cylindrical,  and 
the  circumference  of  its  base  be  ten  feet,  the  depth  of  the  fluid 
in  the  vessel  being  eight  feet,  the  total  surface  of  the  sides  in 
contact  with  the  fluid  is  eighty  square  feet.  The  medium 
pressure  is  that  which  is  sustained  by  a  point  at  the  depth  of 
four  feet,  and,  therefore,  is  equal  to  the  weight  of  four  feet  of  the 
liquid.  Of  the  eighty  square  feet,  forty  are  subject  to  a  less 
pressure  than  this  medium,  and  the  other  forty  are  subject 
to  a  greater  pressure  :  these  two  effects  compensating  each 
other,  the  total  pressure  is  the  same  as  if  the  medium  pressure 
were  diffused  over  the  whole  eighty  feet.  The  whole  lateral 
pressure  is,  therefore,  the  same  as  would  be  produced  upon  the 
bottom  of  a  vessel  of  eighty  square  feet  in  magnitude,  with  per- 
pendicular sides,  and  containing  the  liquid  to  the  depth  of  four 
feet.  This  pressure  would,  in  fact,  be  the  whole  weight  of  the 
fluid  in  the  vessel,  the  quantity  of  which  wouid  be  found  in 
solid  feet  by  multiplying  the  bottom  by  the  depth;  that  is, 
eighty  by  four ;  that  is,  320  solid  feet. 

(24.)  The  rule  deduced  from  this  example,  for  calculating  the 
lateral  pressure,  is  generally  applicable  to  all  cases  where  the 
vessel  containing  the  liquid  has  a  flat  horizontal  bottom  and 
perpendicular  sides.  Find  the  number  of  square  feet  in  the 
sides  below  the  surface  of  the  liquid  contained  in  the  vessel ; 
multiply  that  by  the  number  of  feet  in  half  the  depth  of  the 
liquid :  the  product  will  express  the  number  of  solid  feet  of  the 
liquid,  the  weight  of  which  is  equal  to  the  lateral  pressure. 
The  number  of  square  feet  in  the  sides  may  always  be  found, 
by  multiplying  the  number  of  feet  in  the  circumference  of  the 
bottom  by  the  number  of  feet  in  the  depth  of  the  liquid. 

From  this  rule  some  curious  consequences  follow.  The  pres- 
sure against  the  sides  produced  by  the  liquid  may  exceed  in 
any  proportion,  however  great,  the  whole  weight  of  the  fluid 
which  causes  this  pressure.  If  the  lateral  surface  in  contact 
with  the  fluid  be  double  the  magnitude  of  the  bottom  of  the 
vessel,  then  the  lateral  pressure  will  be  equal  to  the  pressure 
on  the  bottom,  and,  therefore,  equal  to  the  whole  weight  of  the 
fluid ;  for,  in  this  case,  the  lateral  pressure  will  be  equal  to  the 
weight  of  the  fluid  which  would  fill  a  vessel  with  perpendicular 
sides,  having  a  bottom  of  double  the  size,  but  filled  only  to  half 
the  depth.  The  quantity  of  liquid  whose  weight  expresses  the 
3 


A    THBATISE    ON    HYDROSTATICS.  CHAP      III 

ngthe  saTe  Vatio      If  th     Pf    mcreases' the  Pressure  increases 
Fig.  13. 


CHAP.    III.  PRESSURE    ON    VESSELS.  27 

vessel  which  marks  the  surface  of  the  liquid.  Hence,  in  this 
case,  as  well  as  in  the  former,  the  medium  pressure  is  that 
which  affects  the  middle  part  of  the  depth  marked  5.  in  Jig.  14. ; 

Fig.  14. 


and  the  whole  lateral  pressure  will  he  obtained  by  multiplying 
the  number  of  square  feet  on  the  sides  of  the  vessel  by  the 
number  of  feet  in  half  the  depth  of  the  liquid  :  the  product  will 
express  the  number  of  solid  feet  of  the  liquid  whose  weight  is 
equal  to  the  total  pressure.* 

In  this  manner,  the  pressure  on  inclined  embankments,  or  the 
sloping  sides  of  vessels  containing  liquids,  may  be  ascertained. 

In  fig.  14.  the  sides  of  the  vessel  containing  the  liquid  are 
represented  as  sloping  outwards,  or  diverging  upwards  from 
the  bottom  ;  and  it  is  not  difficult  to  conceive,  that  each  point 
of  the  side  will  sustain  a  pressure  equivalent  to  the  weight  of 
the  column  of  liquid  perpendicularly  above  it :  but  the  same 
consequence  would  ensue  if  the  sides  inclined  inwards  or  con- 
verged upwards  from  the  bottom,  as  in  jig.  15.  In  this  case, 


also,  although  each  point  of  the  lateral  surface  have  not  any 
column  of  the  liquid  perpendicularly  over  it,  still  it  is  pressed 
by  the  liquid  in  a  direction  perpendicular  to  the  side,  Avith  the 
same  force  as  if  such  a  column  Avere  perpendicularly  over  it. 
The  cause  of  this  may  be  conceived  by  the  following  reasoning. 
Let  P  be  a  particle  of  the  liquid,  at  the  same  depth  beloAv  the 
surface  as  the  division  marked  5.  on  the  side  of  the  vessel ;  this 
particle  is  evidently  pressed  downwards  by  the  Aveight  of  the 
incumbent  column  P  A.  But,  by  Avlmt  has  been  already  proved, 
it  must  be  pressed  by  the  same  force  in  every  possible  direc- 

*  It  is  necessary  that  the  sides  t-hould  bo  of  uniform  width.  For  example,  the 
above  rule  could  not  bo  applied  to  that  side  of  the  vessel  which  is  presented  to- 
ward the  eye  in  Fig.  11. — AM.  Eu. 


00 

A    TREATISE    ON    HYDROSTATIC*  CHAP     m 

i'  s  may  be  «~- 


Sto  each  of  th       °n  1     °         arm*     Let  water  be  now  P011red 
tached      Tt     "n  ^^      u      '  ^Y  &s  pressure,  the  bottom  is  de- 

^  depth  of^^te^tl^^islTe6^ 


CHAP.    HI. 


PRESSURE    ON    VESSELS. 


There  is  another  method  of  illustrating  these  theorems  ex- 
perimentally, which  is  attended  with  less  practical  difficulty 
than  that  just  mentioned.  Let  the  movable  bottom  be  pressed 
against  each  vessel  by  a  string  attached  to  it,  and  carried  up 
through  the  vessel ;  and  then  let  the  vessel  be  plunged  in  a 
cistern  of  water,  as  represented  in  Jig.  16.,  until  it  attain  such 
a  depth  that  the  upward  pressure  of  the  water  under  the  bottom 
will  be  sufficient  to  keep  the  bottom  firmly  attached  to  the  ves- 
sel. Let  the  string  be  then  disengaged,  and  let  water  be  pour- 
ed into  the  vessel  until  its  pressure  detaches  the  bottom  ;  and 
let  the  depth  of  water  be  observed  which  is  sufficient  to  effect 
this.  Let  each  of  the  three  vessels  be  immersed  in  the  cistern 
in  a  similar  way,  and  to  the  same  depth,  as  represented  'mjigs. 
16, 17,  and  18.  It  will  be  found  that  the  depth  of  water  neces- 


Fig.  16. 


Fig.  17. 


Fig.  18. 


sary  to  be  poured  into  the  vessel  in  order  to  detach  the  bottom 
will  be  the  same. 

The  following  experiment  is  a  very  striking  illustration  of 
the  same  principle  : — 

A  cylindrical  vessel  A  B,  Jig.  19.,  has  a  glass  tube  inserted 
in  it,  water-tight,  at  a,  and  is  provided  with  a  movable  bottom, 
which,  however,  fits  it  water-tight.  This  bottom  is  supported 
by  a  wire,  which,  passing  up  the  tube,  is  attached  to  the  arm  of 
a  balance,  and  is  counterpoised  by  a  weight  in  the  dish  sus- 
pended from  the  other  arm.  Suppose  the  vessel  A  B  now  to 
be  filled  with  water  to  the  neck,  a ;  and  let  the  tube  be  divided 
into  parts  at  6,  c,  d,  e,  each  of  which  shall  be  equal  to  the  depth 
of  the  vessel  A  B.  Let  a  sufficient  weight  be  put  into  the  dish 
to  maintain  the  bottom  of  the  vessel  A  B  in  its  place.  This 
weight  will  be  found  to  be  equal  to  the  weight  of  the  water 
3* 


30 


A    TREATISE    ON    HYDROSTATICS.          CHAP.    III. 


contained  in  the  vessel  A  B.  Thus  it  appears  that  this  water 
presses  down  the  bottom  with  a  force  equal  to  its  weight.  Let 
water  be  now  poured  into  the  tube  until  it  rises  to  the  level  b : 
it  will  be  found  that  exactly  as  much  more  weight  in  the  dish 
D  will  be  necessary  to  maintain  the  bottom  in  its  place,  as  was 
required  to  support  it  when  the  level  was  at  a.  Thus  the 
column  a  6  produces  as  much  pressure  on  the  bottom  as  the 
whole  of  the  liquid  in  the  vessel  A  B.  If  the  tube  be  again  filled 
to  the  level  c,  the  pressure  will  receive  another  increase,  equal 
to  the  weight  of  the  liquid  contained  in  A  B ;  and  a  similar 
addition  must  be  made  to  the  Counterpoise,  in  order  to  main- 
tain the  bottom  of  the  vessel  in  its  place.  In  the  same  manner, 
each  addition  which  is  made  to  the  column  in  the  tube  equal 
to  the  depth  of  the  vessel  A  B  will  cause  a  similar  increase  in 
the  pressure,  and  will  be  indicated  by  the  necessity  of  giving 
a  corresponding  increase  to  the  counterpoise. 

In  this  case  the  box  A  B  and  the  tube  must  be  fixed  in  their 
position  independently  of  the  bottom  of  the  vessel.  The  force 
which  sustains  the  bottom  will  have  a  tendency  to  press  the 
vessel  A  B  upwards,  amounting  to  the  excess  of  the  whole 
weight  in  the  dish  above  the  weight  of  the  bottom  of  the  vessel, 
together  with  the  weight  of  the  water  in  the  vessel  and  tube. 
In  fact,  all  that  part  of  the  weight  in  the  dish  which  is  not  spent 
in  supporting  the  bottom,  and  the  water  above  it,  is  expended 
in  producing  a  pressure  against  the  top  of  the  vessel  A  B,  which 
that  vessel  must  be  so  firmly  fixed  as  to  resist 

(28.)  We  have  hitherto  supposed  the  sides  of  the  vessel  to 
be  straight  and  regular ;  but  even  though  they  be  not,  the  pres- 
sure on  the  bottom  is  determined  by  the  same  rules.  In  the 
consequences  of  this  principle,  the  hydrostatic  paradox  reap- 
pears under  some  curious  forms. 


CHAP.    III. 


PRESSURE    ON    VESSELS. 


Fig.  20. 


Let  ABC  D,^o-.  20.,  be  a  square  close  vessel,  with  a  small 
hole,  O,  in  the  top,  in  which  a  narrow  tube,  T  O,  is  screwed 
water-tight.  Let  the  vessel  A  B  C  D,  and  the  tube  to  the  level 
T,  be  filled  with  water.  According  to  the  principle  which  has 
been  just  established,  the  pressure  on  the  bottom,  C  D,  will  be 
proportional  to  the  depth,  T  M ;  or,  in  fact,  will  be  equal  to  the 
weight  of  water  which  would  fill  a  vessel  of  the  magnitude 
E  D  C  F.  This  will  be  the  case,  however  shallow  the  vessel, 
A  B  C  D,  and  however  narrow  the  tube,  TO,  may  be ;  and 
hence  an  indefinitely  small  quantity  of  water  may  be  made  to 
produce  a  pressure  on  the  bottom  of  the  vessel  which  contains 
it,  equal  to  the  weight  of  any  quantity  of  water,  however  great. 

As  the  pressure  depends  only  on  the  depth,  and  is  independ- 
ent of  the  shape  of  the  vessel,  it  is  not  necessary  that  the  tube, 
T  O,  should  be  straight,  but  it  may  be  bent  or  deflected  into 
any  irregular  form  whatsoever.  But,  whatever  be  its  shape, 
the  depth  of  the  fluid  is  to  be  estimated  by  the  perpendicular 
distance  of  the  upper  surface  from  the  bottom  of  the  vessel. 

(29.)  In  the  examples  already  given,  the  sides  and  bottoms 
of  the  vessels  considered  have  been  flat  surfaces,  or  have  been 
in  the  perpendicular  or  horizontal  position.  The  surfaces, 
however,  of  vessels  or  reservoirs  are  subject  to  every  variety 
and  shape  ;  and  it  is  necessary  in  practical  science  to  possess 
rules  applicable  generally  to  all  surfaces  which  contain  liquids. 
What  has  been  already  stated  with  respect  to  the  average 
pressure,  is  the  principle  which,  generalized,  must  lead  to  such 
a  rule.  The  various  parts  of  any  surface,  whatever  be  its  form, 
will  be  subject  to  pressures,  depending  on  their  depths  below 
the  surface  of  the  liquid,  all  points  at  the  same  depths  suffering 
the  same  pressure.  There  is  a  certain  pressure,  or  mean  of  all 
the  various  pressures,  to  which  the  points  of  the  surface  are 
subject ;  and  whatever  this  pressure  be,  it  must  be  such,  that, 


32  A   TREATISE    ON    HYDROSTATICS.  CHAP.    III. 

if  diffused  over  the  whole  surface,  the  total  amount  of  the  pres- 
sure on  that  surface  will  not  be  altered.  If,  therefore,  this  me- 
dium pressure  can  be  found,  und  the  magnitude  of  the  surface 
in  contact  with  the  liquid  be  known,  the  total  pressure  may 
immediately  be  obtained.  Suppose,  for  example,  the  average 
pressure  be  15  pounds  upon  every  square  inch,  and  that  the 
magnitude  of  the  surface  in  contact  with  the  liquid  be  100 
square  inches,  then  the  total  pressure  will  be  1500  pounds. 

The  determination  of  the  total  pressure,  therefore,  depends 
on  that  of  the  average  pressure.  Now,  as  the  pressure  at  each 
point  is  proportional  to  the  depth  of  that  point  below  the  sur- 
face, it  may  be  considered  as  represented  by  that  depth.  Thus, 
if  a  pressure  of  one  pound  be  produced  upon  a  square  inch  at 
the  depth  of  one  foot,  a  pressure  of  two  pounds  will  be  pro- 
duced upon  a  square  inch  at  the  depth  of  two  feet,  three 
pounds  at  the  depth  of  three  feet,  and  so  on  ;  the  number  of 
feet  in  the  depth  always  expressing  the  number  of  pounds  in 
the  pressure.  Hence  it  is  obvious  that  the  average  pressure 
will  be  produced  at  the  average  depth ;  and,  therefore,  the 
question  is  reduced  to  the  determination  of  the  point  whose 
depth  below  the  surface  is  an  average  of  the  depths  of  all  the 
points  of  the  surface  in  contact  with  the  liquid.  By  a  singular 
though  not  unaccountable  coincidence,  the  point  which  would 
be  the  centre  of  gravity  of  a  thin  sheet  lying  in  close  contact 
with  the  surface  of  the  vessel,  covered  by  the  fluid,  is  placed  at 
that  depth  below  the  surface  which  corresponds  to  the  medium 
pressure.  This  arises  from  a  property  of  the  centre  of  gravity 
well  known  to  geometers,  and  from  which  that  point  has  been 
sometimes  called  the  centre  of  mean  distances.  The  centre 
of  gravity  of  any  surface  is  always  placed  at  a  distance  from 
any  plane  surface,  which  is  an  average  or  mean  of  all  the  dis- 
tances of  the  various  points  of  the  proposed  surface  frcm  the 
plane  surface. 

(30.)  To  determine,  therefore,  the  total  pressure  on  any  sur- 
face, let  the  position  of  the  centre  of  gravity  of  that  surface  be 
determined  by  the  rules  established  in  mechanics,  and  let  its 
depth  below  the  surface  of  the  liquid  be  ascertained ;  then 
multiply  the  number  of  feet  in  this  depth  by  the  number  of 
square  feet  in  the  surface  of  the  vessel  covered  by  the  liquid : 
the  product  will  express  the  number  of  solid  feet  of  the  liquid, 
whose  weight  is  equal  to  the  total  pressure. 

Excepting  the  case  of  regular  surfaces,  the  determination  of 
the  centre  of  gravity  is  a  problem  which  connot  be  solved  with- 
out the  aid  of  mathematical  formularies  of  considerable  difficul- 
ty.* We  shall,  however,  illustrate  the  theorem  just  explained 

*  Cab.  Cyc.  Mechanic*,  chap.  ix. 


CHAP.  III.         PRESSURE  OX  VESSELS.  33 

by  some  examples,  which  we  can  render  intelligible  to  the 
general  reader. 

Let  a  hollow  globe  be  filled  with  a  liquid  through  a  small 
hole  in  the  top.  The  centre  of  gravity  of  the  surface  of  the 
globe  is  evidently  at  its  centre  :  and  therefore  the  depth  of  that 
point  is  half  the  diameter  of  the  globe.  The  total  pressure  will, 
therefore,  be  found  by  multiplying  the  number  of  feet  in  half 
the  diameter  of  the  globe  by  the  number  of  square  feet  in  its 
surface.  By  the  principles  of  geometry  it  is  proved,  that  the 
solid  contents  of  a  globe  are  determined  by  multiplying  the 
number  of  feet  in  half  the  diameter  by  a  third  part  of  the 
number  of  square  feet  in  the  surface.  Hence  it  appears  that 
the  pressure  on  the  surface  of  the  globe  is  three  times  the 
weight  of  its  contents. 

If  a  cubical  vessel — that  is,  one  having  a  square  bottom  and 
four  square  side?,  each  equal  to  the  bottom — be  filled  with  a 
fluid,  the  centre  of  gravity  of  each  of  the  four  perpendicular 
sides  will  be  at  half  the  entire  depth  of  the  fluid  below  the  sur- 
face. Therefore  the?  pressure  on  each  side  will  be  found  by 
multiplying  the  number  of  feet  in  half  the  depth  by  the  number 
of  square  feet  in  the  side.  But  the  entire  contents  of  the  ves- 
sel are  found  by  multiplying  the  number  of  feet  in  the  entire 
depth  by  the  number  of  square  feet  in  any  side.  Hence  it  ap- 
pears that  the  pressure  on  each  of  the  four  sides  is  equal  to 
half  the  weight  of  the  fluid  contained  in  the  vessel.  The  pres- 
sure on  alPthe  four  sides  is,  therefore,  equal  to  twice  the 
weight  of  the  fluid  contained  in  the  vessel.  The  pressure  on 
the  bottom  has  already  been  shown  to  be  equal  to  the  whole 
weight  of  the  fluid :  and  therefore  it  follows,  that  the  total 
pressure  of  the  fluid  on  the  surface  of  the  vessel,  including  both 
the  sides  and  bottom,  is  equal  to  three  times  the  weight  of  the 
fluid  which  it  contains. 

Thus  it  appears,  that  a  globe  and  a  cube,  containing  equal 
measures  of  liquid,  will  suffer  equal  pressures  if  filled,  each 
sustaining  a  pressure  amounting  to  three  times  the  weight  of 
the  fluid  it  contains. 

(31.)  If  any  body  be  immersed  in  a  fluid,  the  pressure  which 
its  surface  sustains  from  the  surrounding  liquid  is  .to  be  deter- 
mined by  the  same  rules,  and  according  to  the  same  methods, 
as  are  used  for  determining  the  pressure  on  the  surface  of  the 
vessel  which  contains  the  liquid.  Thus,  if  a  globe  be  plunged 
in  a  liquid,  the  total  pressure  on  its  surface  is  found  by  multi- 
plying the  number  of  feet  in  the  depth  of  its  centre,  below  the 
surface  of  the  liquid,  by  the  number  of  square  feet  in  its  exte- 
rior surface. 

(32.)  The  two  hydrostatical  theorems  which  we  have  at 


A    TREATISE    ON    HYDROSTATICS.          CHAP.    Hf. 

tempted  to  explain  in  this  and  the  preceding  chapter,—  viz  J 
That  liquids  transmit  pressure  equally  in  all  directions  ;  Ind,  2. 
That  the  pressure  produced  by  the  weight  of  a  liquid  is  pro- 

serve  to  elucidate  -5r*tt 

If  an  empty  bottle,  or  rather  one  containing  only  air   be 
Sde  ablTf  iand  ?iC  SUnk  by  WGights  attached  t°  *  ^  a  con! 
water  will  p?th  *Y  V^'  ^  prGSSUre  °f  the  surrounding 
Jhrmmh   L        I'  brneak  the  bottle,  or  force  the  cork  into  it 
to  i?  Ill  ^    "I    '     °n  dra™£  UP  the  b°ttle,  ^  ™n  be  found 


to  i       ll  ,      ™ 

the  neck?  ^^  ^  t0  haVG  the  Cork  within 


ho1  brnLn0^  If™  ^  SideS'  and  be  sq«^e-bottomed,  it  will 
be  br^en  by  the  pressure,  the  form  being  unfavorable  to 
strength  ;  but  if  it  be  round,  it  will  be  more  iFkely  to  resist  the 
pressure,  and  to  have  the  cork  forced  in.  The  ^hapen  this 
case  is  conducive  to  strength,  partaking  of  the  qualities  of  an 

An  experiment  of  the  nature  just  described  was  made  by  Mr 
Campbell,  author  of"  Travels  in  the  South  of  Afrka  »     On  1  is 

3  fnt  T  th\Ca/e  ?f  ?°°d  H°P6  homeward,  he  forced  a 

l       H    ,t  ?|Cik  °f  a  b°ttle'  so  thick  as  to  fit  ^  very  tightly 

and  so  that  half  the  cork  remained  above  the  edge  of  the  neck' 

of  Ct°hre  1WS  51  r°UIld  1th6  C°rk'  and  fa8tened  to  ^e  neck 

J  bottle  ;  and  the  whole  was  covered  with  pitch.  The 

bottle  was  connected  with  a  weight  to  make  it  sink,  and,  beino- 
uspended  by  a  sounding-line,  was  gradually  let  down  into  thf 
ea.  When  it  attained  the  depth  of  about  fifty  fathoms,  an  in- 

crease of  weight  was  suddenly  felt.     Upon  drawing  up  the  hot- 

«e  the  cork  was  found  inside,  and  the  bottle  filled  with  water. 


Another  bottle  was  similarly  corked,  but  a  sail-needle  was 
passed  through  the  cork  across  the  edge  of  the  neck  so  aT 
resist  the  passage  of  the  cork  into  the  bottle.     Thus  prepared 
the  bottle  was  again  immersed  to  the  depth  of  fifty  Son"  s 
and  the  same  sudden  increase  of  weight  was  felt.     Upon  draw 
ing  up  the  bottle  it  was  found  fillecf  with  water,  but  the  cork 
was  not  displaced.     Mr.  Campbell  attributed  this  effect  to  the 


CHAP.    III.  COMPRESSION    OP    LIQUIDS.  35 

which  covered  it  not  being  broken,  arose  from  the  perfectly 
equal  pressure  which  was  excited  upon  it  in  all  directions.* 

The  equality  of  the  pressure  which  a  liquid  exerts  in  all  di- 
rections is  demonstrated  by  the  fact,  that,  to  whatever  depth  a 
soft  or  brittle  substance  may  be  immersed,  it  will  undergo  no 
change  of  shape  by  the  surrounding  pressure.  This  is  an  effect 
which  it  is  obvious  could  not  be  produced  by  any  other  cause 
than  a  perfect  equality  of  pressure  on  every  part ;  for  if  any 
part  were  subject  to  a  greater  force  than  an  adjacent  part,  that 
part  would  be  pressed  inwards  if  the  body  were  soft,  and  would 
be  broken  off  if  it  were  brittle.  A  piece  of  soft  wax,  or  a  piece 
of  glass  not  having  any  hollow  part  within  it,  being  immersed 
to  any  depth  in  water,  suffers  no  change. 

If  a  piece  of  wood  which  floats  on  water  be  forced  down  to 
a  great  depth  in  the  sea,  the  pressure  of  the  surrounding  liquid 
will  be  so  severe,  that  a  quantity  of  water  will  be  forced  into 
the  pores  of  the  wood,  which  will  be  sufficient  to  increase  its 
weight,  so  that  it  will  be  no  longer  capable  of  floating  or  rising 
to  the  surface/)- 

A  diver  may,  with  impunity,  plunge  to  certain  depths  in  the 
sea ;  but  there  is  a  limit  of  depth  beyond  which  he  cannot  con- 
tinue to  live  under  the  pressure  to  which  he  is  subject.  For 
the  same  reason,  it  is  probable  that  there  is  a  depth  below 
which  fishes  cannot  exist-! 

(33.)  Liquids  in  general  are  treated  in  hydrostatics  as  incom- 
pressible bodies  ;  that  is,  as  bodies  which,  being  submitted  to 
pressure,  will  not  suffer  their  dimensions  to  be  diminished ;  and 
this  is  true,  except  in  extreme  cases.  It  was  long  considered 
that  no  force  whatever  was  capable  of  compressing  a  liquid ; 
but  experiments  instituted  in  the  year  1761  by  Canton  proved, 
Fig.  21.  that  under  severe  pressure  they  suffered  a  slight 
diminution  of  bulk :  it  also  appeared,  that  upon  the 
pressure  being  removed  they  resumed  their  former 
dimensions.  It  was  thus  established,  that  liquids  not 
only  were  compressible  in  a  slight  degree,  but  also 
elastic.^ 

The  pressure  of  liquids  at  great  depths  below  the 
surface,  furnishes  an  easy  method  of  verifying  by  ex- 
periments these  results.  Let  A  B,  Jig.  21.  b'e  a  cy- 
lindrical  vessel,  having  a  round  hole,  C,  in  the  top, 

*  Campbell's  Travels,  p.  507.     Brewster's  Ency.  xi.  p.  483. 

•f  Hence  the  timbers  of  ships,  which  have  foundered  in  a  deep  part  of  the  ocean, 
never  rise  again  to  the  surface,  like  those  which  are  sunk  near  tho  shore. — 
AM.  ED. 

J  Fishes  have  been  caught  at  a  depth  at  which  they  must  have  sustained 
a  pressure  of  eighty  tons  on  each  square  foot  of  the  surface  of  their  bodies. — 
AM.  EQ. 

§  Cab.  Cyc.  Mechanics,  p.  19. 


nf» 

A    TREATISE    ON    HYDROSTATICS.          CHAP.    HI. 

through  which  a  piston,  P  M,  passes  water-tight.     Let  this  vessel 

it'  C  Le?  fri  y  m  ft*  WHh  ATr'  the  Pist°n  P  M  ^ing  inserledt 
£  j£  £  f  S  r  n6  UP?nthQ  Plston'  with  efficient  friction  to 
down  f  \£r°m  f  m&  br  **  own  weight;  and  let  it  be  pressed 
down  to  the  orifice  C.  Let  the  vessel  now  be  plunged  to 

SSfe%  Pth  ^  the  S6a-  Up°n  dra™S  «  «R  S  wil  be 
found  hat  the  pressure  of  the  surrounding  water  had  forced  the 

tatoed  i°na/reat<;!;  ^  *  ^  V6SSel  ;  and  that  the  water  *£ 
Th]s  w  H  KeTd  r/T  \0mPressed  into  smaller  dimensions. 

is  will  be  indicated  by  the  position  of  the  rin^  which  si 
on  the  piston;  for  that  will  be  "found,  not  at  thforTfi  e,  a    be! 

fn^  T  r!L°n'  but  f  a  Certain  distance  ab°ve  it.  On  being 
forced  into  the  vessel,  the  piston  passed  through  the  ring  which 

SSr^SSSi1"  1S  P°Siti0n  ^  thG  10P  °f  the  -ssel  frnmedt 
ately  surrounding  the  piston.  Upon  drawing  up  the  vessel 

the  removal  of  the  pressure  enabled  the  wat?r  contained  in  it 
LteSeionS  dirn"°nS'  and  the  Pist°n  Was  forLf  baTk  to  i  s 
fv^th?  ?n  S'  f  S,"  r"?  °Ut  °f  the  V6SSel  i1:  carried  the  rinS  "P 
the  vessel  1  ad  V  H^06  °f  ?6  ring  fr°m  the  hole  C'  after 


ha    b  2? 


v  of  waefpm°StT?T,Veili.ent  Practical  Proof  of  the  compres- 
7     atefr*     Jt  hkewise  establishes  the  elasticity  of  that 

the  niton  wrrefmere,ly-C°mpreSsible'  without  be^n^  S 
tic,  me  piston  when  forced  into  the  vessel  would  remain  in  it 

volume'  ^CTMC1,^dcon^uetoretoi™SiS^ 
Tho  dP.  the,force  ^ich  compressed  it  had  been  removed, 
1  he  degree  of  compression  produced  by  a  given  force  mav 

m^Se^t^T  tht  t0tal  C°ntents  of  the  vessel';^ 

tne  wate    Contained  m  the  vessel  is  diminished  by  one  twenti- 
'  dl™ensions'     Thu«  20  solid  inches  of  water 

°f  sea 


Pen  to  c°mmunicate  with  an 


interalvitvo  c°mmuncate  wt    an 

case  be  proportional  to  the  depth  of  the  cavity  belo7  the  top 


CHAP.  IV.          LIQUIDS    MAINTAIN    THEIR   LEVEL.  37 

(35.)  In  the  construction  of  pipes  for  the  supply  of  water  to 
cities,  it  is  necessary  that  those  parts,  which  are  much  below 
the  level  of  the  reservoir  from  which  the  water  is  supplied, 
should  have  a  greater  strength  than  is  requisite  in  those  which 
are  in  more  elevated  situations.  A  pressure  always  acts  upon 
the  inner  surface  of  the  pipe,  tending  to  hurst  it,  which  may  be 
estimated  in  the  manner  already  explained.  A  pipe,  the  di- 
ameter of  whose  bore  is  4  inches,  has  an  internal  circumfer- 
ence of  about  1  foot,  and  the  internal  surface  of  1  foot  of  such 
a  pipe  will  be  1  square  foot  or  144  square  inches.  If  such  a 
pipe  were  140  feet  below  the  level  of  the  reservoir,  it  would 
therefore  suffer  a  bursting  pressure,  amounting  to  about  60 
pounds  on  every  square  inch  of  its  surface,  for  28  inches  is  con- 
tained 60  times  in  140  feet ;  and  hence  a  piece  of  the  pipe  1 
foot  long"  will  sustain  144  times  this  pressure,  that  is,  a  bursting 
pressure  of  8640  pounds.  This  pressure  considerably  exceeds 
&••'  oduced  in  most  high  pressure  steam  engines.  , 


CHAP.  IV. 

S  MAINTAIN  THEIR  LEVEL. 


EXPERIMENTAL  PROOFS.  —  VESSEL  CONNECTED  WITH  COMMUNICATING 
TUBE.  —  SEVERAL  VESSELS  BETWEEN  WHICH  THERE  IS  A  FREE  COM- 
MUNICATION. —  HYDROSTATIC  PARADOX  EXPLAINED  BY  THIS  PRINCI- 
PLE.— SURFACE  OF  A  LIQUID  LEVEL.  —  WHY  THE  QUALITY  DOES  NOT 
EXTEND  TO  SOLIDS.—  SURFACE  OF  THE  LAND.  —  SURFACE  OF  THE 
SEA.  —  CURIOUS  OPTICAL  DECEPTION  IN  WAVES.  —  SIMILAR  PROPER- 
TY IN  REVOLVING  SCREW.—  ORNAMENTAL  FOUNTAIN  CLOCKS.  — 
PHENOMENA  OF  RIVERS,  SPRINGS,  WELLS,  CATARACTS,  EXPLAINED.  — 
CANALS,  LOCKS.  —  METHOD  OF  SUPPLYING  WATER  TO  TOWNS.  —  EXACT 
SENSE  OF  THE  WORD  LEVEL.—  COMMON  SURFACE  OF  TWO  LIQUIDS 
IN  THE  SAME  VESSEL.  —  LEVELING  INSTRUMENTS.  —  SPIRIT  LEVEL. 

(36.)  FROM  the  two  properties  of  liquids  established  in  the  last 
two  chapters,  a  third,  and  not  less  important  one,  may  be  de- 
duced. If  the  pressure  arising  from  the  weight  of  a  liquid  be 
proportional  to  the  depth,  and  that  pressure  be  transmitted 
equally  in  every  possible  direction,  it  will  follow,  that  the  sur- 
face of  all  parts  of  a  liquid  contained  in  the  same  vessel,  or  in 
two  or  more  vessels  between  which  there  is  a  free  communica- 
tion by  tubes  or  pipes,  or  otherwise,  must  be  always  at  the  same 
level  ;  and  that  if  any  external  cause  accidentally  disturb  that 
level,  the  liquid  will  by  its  gravity  return  to  it,  the  higher  parts 
falling,  and  the  lower  parts  rising,  until  the  equality  be  re- 
stored. 

4 


38 


A    TREATISE    ON    HYDROSTATICS. 


CHAP.  IV. 


Let  A  B  and  A'  B',  Jig.  22.,  be  two  perpen- 
dicular glass  tubes,  united  by  a  third  tube,  B  B', 
placed  in  a  horizontal  position.  Let  any  liquid 
be  poured  into  the  tube  A  until  the  horizontal 
tube  B  B'  is  rilled.  Let  us  now  suppose^  that 
the  lower  end  of  the  tube  A/  B'  is  closed  by 
a  stopcock  at  B'.  The  tube  B  B'  being  hori- 
zontal, the  water  which  fills  it  has  no  ten- 
dency to  move  by  its  weight  towards  either  end,  and  therefore 
ie  stopcock  at  B'  sustains  no  pressure  from  it.  Let  an  addi- 
tional quantity  of  the  liquid  be  now  poured  in  at  A  until  it  fill 
the  tube  to  the  height  C.  The  surface  of  the  liquid  in  the  hor- 
izontal tube  at  B  is  now  pressed  by  the  weight  of  the  column 
B  U  i  he  liquid  in  the  horizontal  tube  transmits  this  pressure 
undimmished  to  the  stopcock  B',  which  is  therefore  pressed  up- 
wards by  a  force  equal  to  the  weight  of  the  column  of  liquid 
±i  U.  1  his  pressure  would  evidently  cause  the  liquid  in  the 
horizontal  tube  to  rush  into  the  vertical  tube  B'  C'  if  the  stop- 
cock B'  were  opened.  Supposing  it  to  remain  closed,  however 
let  a  quantity  of  the  liquid  be  poured  in  at  A!  until  the  column 
J  shall  attain  the  same  height  as  the  column  B  C  ;  the  stop- 
cock B'  will  then  be  pressed  downwards  by  the  weight  of  the 
column  B'  C'  resting  upon  it,  while  it  is  at  the  same  time  press- 
id  upwards  by  the  weight  of  the  column  B  C,  transmitted  to  it 
by  the  liquid  in  the  horizontal  tube.  It  is  thus  pressed  up- 
Avards  and  downwards  by  equal  forces  ;  and  therefore,  if  it 
were  free  to  move,  it  would  have  no  tendency  to  change  its 
P°s^lon  :  hence,  if  the  stopcock  B'  be  opened,  and  the  column 
B  U  allowed  to  rest  immediately  on  the  surface  of  the  liquid, 
it  will  be  supported,  and  no  motion  will  take  place  ;  thus  the 
columns  B  C  and  B'  C',  having  equal  heights,  balance  each 
other  through  the  medium  of  the  liquid  in  the  horizontal  tube. 
Fig.  23.  Let  us  suppose  the  stopcock  B',/g.  23.,  again 

closed,  and  let  the  column  of  liquid  in  B7  A'  be 
greater  than  the  column  of  liquid  in  B  A,  so 
that  C'  will  be  higher  than  C.  The  stopcock  at 
B'  will  now  be  pressed  downwards  by  the  weight 
of  the  column  B'  C',  and  it  will  be  pressed  up- 
£l«  wards  by  the  weight  of  the  column  B  C.  The 
downward  pressure  being  therefore  greater  than 
the  upward,  if  the  stopcock  be  opened,  the  column  B'  C'  will 
descend,  and  the  column  B  C  will  be  forced  up.  The  level  C' 
will  therefore  fall,  and  the  level  C  will  rise.  When  they  attain 
the  same  height,  their  weights  will  mutually  balance  each  other, 
as  in  Jig.  22. ;  and  if  these  were  the  only  forces  in  action,  all 

S°r^0n  WOUld  then  cease*     ?ut  in  the  descent  of  the  column 
U  &  the  whole  mass  of  liquid  in  the  tubes  has  acquired  a  cer 


CHAP.    IV.          LIQUIDS    MAINTAIN    THEIR   LEVEL.  39 

tain  velocity,  which,  by  reason  of  its  inertia,*  it  has  a  disposi- 
tion to  retain.  The  level  C  will  therefore  continue  to  rise,  and 
the  level  Cf  to  fall,  after  they  have  attained  the  same  height; 
but  when  the  column  B  C  becomes  higher  than  B'  C'  its  down- 
ward pressure  exceeds  the  upward  pressure  transmitted  to  it 
from  B'  C',  and  this  excess  resists  the  tendency  to  continue  its 
motion  upwards,  and  finally  destroys  it.  The  level  C  will  then 
begin  to  descend,  and  the  level  C'  to  rise,  and  this  will  continue 
until  the  level  C'  has  attained  the  height  which  it  had  at  the 
commencement  of  the  process  ;  it  will  then  fall,  and  the  oscil- 
lation will  continue. 

We  have  here,  however,  set  aside  the"consideration  of  the 
effects  of  the  friction  between  the  liquid  and  the  tubes  which 
contain  it.  This,  by  continually  resisting  the  motion  of  the  li- 
quid, will  cause  it  to  rise  to  a  less  height  in  the  tubes,  at  each 
oscillation,  than  it  did  at  the  preceding  one,  and  at  length  will 
reduce  it  to  a  state  of  rest.  In  this  state  the  surfaces  C  C'  will 
be  at  equal  heights  above  the  horizontal  tube  B  B'. 


(37.)  We  have  hitherto  supposed  the  tubes  A  B  and  A'  B'  to 
be  perpendicular,  but  the  same  consequences  will  ensue  if  they 
have  any  oblique  position,  as  in  Jig.  24.  As  before,  let  a  stop- 
cock be  placed  at  B'  and  closed ;  let  the  horizontal  tube  B  B' 
be  filled  with  liquid,  and  let  a  column  be  also  poured  into  the 
oblique  tube  A  B,  the  surface  of  which  is  at  C.  According  to 
what  has  been  proved  in  the  last  chapter,  the  column  B  C 
presses  on  the  liquid  in  the  horizontal  tube  with  a  force  propor- 
tioned to  the  perpendicular  height  of  the  surface  C  above  B. 
In  fact,  it  presses  with  a  force  equal  to  the  weight  of  a  column 
whose  height  is  B  D,  the  line  drawn  from  B  perpendicular  to 
the  horizontal  line  from  C.  This  pressure,  therefore,  is  trans- 
mitted by  the  liquid  in  the  horizontal  tube  to  the  stopcock  Br, 
which  is  pressed  in  the  direction  of  the  tube  B'  A'  with  that 
force.  If  a  quantity  of  liquid  be  now  poured  in  at  A',  until  the 
height  of  the  surface  C'  above  B'  be  equal  to  the  height  of  the 
surface  C  above  B,  the  downward  pressure  on  B'  will  be  equal 
to  the  upward  pressure  transmitted  from  the  column  B  C  ;  for 
this  downward  pressure  is  equal  to  the  weight  of  a  column 
whoss  height  is  B'  D',  which  is  equal  to  B  D, 

Cab.  Cyc.  Mechanics,  p.  21.  et  scq. 


40  A  TREATISE    OX    HYDROSTATICS.  CHAP.  IV. 

By  reasoning  precisely  similar  to  that  which  has  been  used 
with  respect  to  the  perpendicular  tubes,  it  may  be  proved,  that 
if  the  stopcock  B'  be  opened,  the  liquid  will  remain  at  rest ; 
and  also  that  if  the  surface  C'  be  not  at  the  same  level  with  the 
surface  C,  an  oscillation  will  take  place,  which  being  continued 
for  a  certain  time,  the  surfaces  will  at  length  settle  at  the  same 
height  above  the  horizontal  tube. 

(38.)  We  have  hitherto  supposed  that  the  tubes  containing 
the  liquid,  whose  weight  produces  the  pressure,  are  equal  in 
bore.  The  same  consequences  may,  however,  be  deduced,  if 
they  be  unequal,  or  if,  instead  of  being  tubes,  they  be  vessels 
of  any  form  whatever.  Let  A  B,  Jig.  25.,  be  an  oblique  tube 

Fig.  25. 


communicating  with  a  reservoir  A'  B',  a  stopcock  being  placed 
at  B'.  Let  the  tube  and  reservoir  be  now  filled  to  the  same 
height,  C  C',  the  stopcock  at  B'  being  closed.  The  same  hori- 
zontal line,  C  C',  will  mark  the  level  of  the  liquid  in  the  tube, 
and  the  liquid  in  the  reservoir.  The  liquid  B  C,  in  the  tube 
B  A,  will  press  on  the  liquid  in  the  horizontal  tube,  with  a  force 
equal  to  the  weight  of  a  column  of  the  liquid  whose  height  is 
B  D,  and  whose  base  is  equal  to  the  section  of  the  tube  at  B. 
This  force  will  be  transmitted  by  the  liquid  in  the  horizontal 
channel  B  B',  so  that  each  square  inch  of  the  surface  of  the 
stopcock  B'  will  be  pressed  by  a  forco  equal  to  the  weight  of  a 
column  whose  base  is  a  square  inch,  and  whose  fieight  is  equal 
to  B  D.  The  liquid  in  the  vessel  A'  B'  presses  on  each  square 
inch  of  the  other  side  of  the  stopcock,  with  a  force  which  is 
equal  to  the  weight  of  a  column  whose  base  is  a  square  inch, 
and  whose  height  is  B'  D'.  If,  therefore,  as  we  have  already 
supposed,  B1'  D'  be  equal  to  B  D,  the  stopcock  will  be  pressed 
equally  on  both  sides  ;  and  if  it  be  opened,  no  motion  will  take 
place  in  the  liquid.  But  if,  on  the  other  hand,  B'  D'  be  not 
equal  to  B  D,  the  higher  surface  will  subside,  and  the  lower 
one  rise,  and  the  oscillating  motion  already  described  will  en- 
sue, and  will  continue  until,  at  length,  the  surfaces  C  and  C' 
settle  at  the  same  level. 

An  apparatus,  to  illustrate  experimentally  the  property  by 
which  liquids  maintain  the  same  level  in  communicating  vessels, 


CHAP.    IV.          LIQUIDS    MAINTAIN    THEIR    LEVEL.  4J 

is  represented  in  Jig.  26.  A,  B,  C,  D,  E,  are  glass  vessels,  of 
various  shapes,  communicating  by  short  tubular  shanks  with  a 
horizontal  tube,  which  passes  beneath  them,  and  which  in  the 


figure  is  concealed  by  the  stand  which  supports  the  vessels.  In 
the  shank  of  each  is  placed  a  stopcock,  K,  which  when  closed 
insulates  the  vessels,  and  when  opened  leaves  a  free  communi- 
cation between  them  by  means  of  the  tube.  Let  all  the  stop- 
cocks be  now  closed,  and  let  water  be  poured  into  the  several 
vessels,  so  as  to  stand  at  different  heights :  if  the  several  stop- 
cocks be  opened,  so  that  the  vessels  shall  have  a  free  commu- 
nication with  each  other,  the  higher  surfaces  will  fall,  and  the 
lower  ones  rise,  until  they  attain  the  same  level,  and  then  all 
motion  will  cease.  If  the  stopcocks  be  again  closed,  and  water 
poured  into  the  vessels,  so  as  to  give  the  liquids  different  levels, 
the  experiment  may  be  repeated  by  opening  the  stopcocks.  It 
will  always  be  found,  that,  when  the  stopcocks  are  opene'd,  the 
liquid  will  settle  itself  to  the  same  level  in  all  the  vessels. 

A  teapot,  kettle,  or  any  other  vessel  containing  a  liquid,  and 
having  a  spout,  must  be  so  constructed  that  the  lip  of  the  spout 
shall  be  on  a  level  with  the  top  of  the  vessel,  or  at  least  on  a 
level  with  the  highest  point  to  which  the  vessel  is  to  be  filled  ; 
otherwise,  upon  filling  the  vessel  above  the  level  of  the  end  of 
the  spout,  the  liquid  in  the  vessel,  having  a  tendency  to  rise 
above  the  level  of  the  end  of  the  spout,  will  issue  from  it.  If 
the  vessel  be  inclined  with  the  spout  downwards,  it  takes  a  po- 
sition in  which  the  level  of  the  water  in  the  vessel  is  above  that 
of  the  lip  of  the  spout,  and  accordingly  the  liquid  flows  out. 

(39.)  Various  examples  of  that  class  of  effects  which  have 
been  called  the  Hydrostatic  Paradox,  and  which  have  been  al- 
ready noticed,  may  be  shown  to  be  equivalent  to  this  property 
by  which  fluids  maintain  their  level.  We  shall  confine  our- 
selves here  to  one  example.  Let  ABC  D,  ./!§•.  27.,  be  a  large 
vessel,  with  perpendicular  sides,  and  communicating  by  B  E 
with  a  perpendicular  tube,  E  F,  If  water  be  poured  into 
A  B  C  D  until  it  rises  to  the  level  K  L,  it  will  stand  at  the 
same  level,  H,  in  the  tube  E  F. 

Now,  snppos?  all  the  water  in  the  vessel  A  B  C  D  above  tha 


A  TREATISE  ON  HYDROSTATICS. 


CHAP.  IV. 


level  IVI  N  to  be  removed,  and  its  place  supplied  by  a  piston, 
M  N,  which  moves  water-tight  in  the  vessel ;  and  let  this  piston 
be  loaded  with  weights,  so  that  the  weight  of  itself  and  its  load 


shall  be  equal  to  the  weight  of  the  water  which  has  been  re- 
moved :  the  piston  will  then  press  on  the  water  below  it  with 
the  same  force  as  the  water  removed  previously  pressed  upon 
it ;  and  as  the  water  removed  was  sustained  by  it,  the  piston 
with  its  load  will  also  be  sustained.  Thus  it  appears,  that  this 
piston  is  supported  by  the  pressure  of  tile  column  of  water  in 
E  F.  It  will  easily  be  perceived  thut  this  is  identical  with  the 
hydrostatic  bellows  explained  in  (8.). 

If  the  column  of  water  in  the  tube  above  the  level  O  be  re- 
moved, and  its  place  supplied  by  a  piston  of  equal  weight,  this 
piston,  O,  will  support  the  groat  piston  M  N.  This  effect  is 
equivalent  to  the  principle  of  the  hydrostatic  press  explained 
in  (7.). 

(40.)  After  what  has  been  already  proved,  it  is  nearly  self- 
evident  that  every  part  of  the  surface  of  a  fluid  confined  in  a 
vessel  must,  if  at  rest,  bo  at  the  same  level.  If  this  were  not 
the  case,  it  would  evidently  be  possible  that  the  surfaces  of  the 
same  fluid,  in  communicating  vessels,  might  have  different 
levels  ;  for  if  we  suppose  two  different  parts  of  the  surface  of  a 
liquid  in  a  vessel  to  have  different  heights,  as  represented  in 
the  vessel  ABC  T>,Jig.  28.,  let  us  divide  the  vessel  into  two 

Fig.  28. 


by  a  solid  partition,  E  P,  leaving,  however,  between  the  two 
parts,  .a  communication,  O,  at  the  bottom  ;  and  let  this  partition 


CHAP.    IV.  MOUNTAINS    AND    VALLEYS.  43 

so  divide  the  liquid,  that  the  higher  part  of  the  surface,  H,  shall 
occupy  one  division,  and  the  lower  part,  L,  the  other.  We 
should  thus  have  a  liquid  in  communicating  vessels  standing  at 
different  levels  ;  a  result  which  would  be  inconsistent  with 
what  was  formerly  proved.  Therefore  it  follows,  that  all  parts 
of  the  surface  of  a  liquid  contained  in  any  vessel  must  stand  at 
the  same  level  when  at  rest. 

Indeed,  this  theorem  is  nothing  more  than  a  manifestation  of 
the  tendency  of  the  component  parts  of  every  body  to  fall  into 
the  lowest  position  which  the  nature  of  their  mutual  connection, 
and  the  circumstances  in  which  they  are  placed,  admit.  Moun- 
tains do  not  sink  and  press  up  the  adjacent  valleys,  because  the 
strong  cohesive  principle  which  binds  together  the  constituent 
particles  of  their  masses,  and  those  of  the  earth  beneath  them, 
is  opposed  to  the  force  of  their  gravity,  and  is  much  more  pow- 
erful :  but  if  this  cohesion  were  dissolved,  these  great  eleva- 
tions would  sink  from  their  lofty  eminences,  and  the  interven- 
ing valleys  would  in  their  turn  rise — an  interchange  of  form 
taking  place  ;  and  this  undulation  would  continue  until  the 
whole  mass  would  attain  a  state  of  rest,  when  no  inequality  of 
height  would  remain.  All  the  inequalities,  therefore,  observa- 
ble on  the  surface  of  land,  are  owing  to  the  predominance  of 
the  cohesive  over  the  gravitative  principle  ;  the  former  depriv- 
ing the  earth  of  the  power  of  transmitting,  equally  and  in  every 
direction,  the  pressure  produced  by  the  latter. 

On  the  other  hand,  if  the  sea,  when  in  a  state  of  agitation, 
were  suddenly  congealed,  the  cohesive  principle  taking  a  strong 
effect,  the  mass  of  water  would  lose  the  power  of  transmitting 
pressure,  and  those  inequalities  which,  in  the  liquid  form,  were 
fluctuating,  would  become  fixed  ;  every  wave  would  be  a  hill, 
and  the  intermediate  space  a  valley. 

There  is  a  curious  optical  deception  attending  the  alternate 
elevation  and  depression  of  the  surface  of  a  liquid,  which  it  may 
be  useful  here  to  notice.  The  waves  thus  produced  appear  to 
have  a  progressive  motion,  which  is  commonly  attributed  to  the 
liquid  itself.  When  we  perceive  the  waves  of  the  sea  appar- 
ently advancing  in  a  certain  direction,  we  are  irresistibly  im- 
pressed with  a  notion  that  the  sea  itself  is  advancing  in  that 
direction.  We  consider  that  the  same  wave,  as  it  advances,  is 
ccmposed-of  the  same  water,  and  that  the  whole  surface  of  the 
liquid  is  in  a  state  of  progressive  motion.  A  slight  reflection, 
however,  on  the  consequences  of  such  a  supposition,  will  soon 
convince  us  that  it  is  unfounded.  The  ship  which  floats  upon 
the  waves  is  not  carried  forward  with  them ;  they  pass  beneath 
her,  now  lifting  her  on  their  summits,  and  now  letting  her  sink 
into  the  abyss  between.  Observe  a  sea  fowl  floating  on  the 
water,  and  the  same  effect  will  be  seen.  If,  however,  the  wa- 


41 


A  TIU  VTIM    ON  n\  DROS1  il  H  « 


(  HAl*.   IV. 


tor  itself  partook  of  the  motion  which  wo  ascribe  to  its  wave*, 
tho  ship  and  tho  foul  would  each  bo  carried  for\\  aid,  and  would 
I  motion  in  common  with  tho  liquid.  Once  on  tho  summit 
of  a  wave,  thoro  thoy  would  continually  vomain,  and  their  mo- 
tion \\ould  ho  as  smooth  as  if  thoy  \\orepropelloduponthecalm 
snrt'aoo  of  a  lako.  Or  if  once  in  tho  vailoy  between  two  ^ 

likewise  thoy  would  continually  remain,  the  ono  wa\o 
continually  preceding  thom  and  the  othor  follo^ 

In  liko  inannor,  if  \\  o  observe  tho  waves  continually  npproai'h- 
injr  tho  sluuv,  wo  must  bo  oonvnu'od  that  this  apparont  motion 
is  iu>t  ono  in  which  tho  water  has  any  share  ;  for  uoro  it  so,  tho 
waters  of  the  son  \\onlu  soon  bo  lumped  upon  tho  shores,  and 
would  inundate  the  adjacent  country  :  but  so  far  from  the  wa- 
ters partaking  of  tho  apparent  motion  of  the  waves  in  approach- 
ing the  shore,  this  motion  of  tho  uavos  ccntinues,  oven  when 
.ire  retiring.  If  wo  observe  a  tlat  strand  when  tho 
tide  is  ebb;-  -.11  still  find  tho  waves  moving1  towards  tho 

shore. 

Th;>t  the  apparent  motion  of  the  \\aves  is,  therefore,  an  illu- 
vvo  can  no  louder  doubt  ;  but  we  are  naturally  curious  to 
kuo\\    what  is  tho  causo  of  this  illusion.     Thnt   a   proj:'.. 

•.  t.ikos  place  in  .«>Mj»7/ii.'?ir.  wo  have  proof,  from  tho  ovi- 
fience  of  sijfht  That  no  pro^rossi\o  motion  takes  place  in  tho 
luniid,  wo  have  also  proof,  both  from  the  end;-  t,  and 

from  othor  still  more  unquestionable  testimev,\ .  To  \\hat  then 
iloOvS  Uu>  motion  bolonjr  ?  \Vo  answer,  tv>  the/o;v;j  of  the  \\ ,  \  D, 
and  tu»t  to  tho  liquid  \\hich  composes  it 


K.      K.' 


ru 


Let  tho  ummlatinjT  line  in  fs;.  Q$>.  bo  supposed  to  rep- 
tho  surface  of  the  sea,  nnd  lot'A  1U'  bo  tho  crests  of  thn 
cessive    wnvos,  and   a  b  c   tho   intermediate   valleys'    lot    LM 
Wpresont  the  bottom  of  the  SCau      At    \.  •  fthc  water 

i*  represented  by  tho  lino  A  K 
and  tho  tleptli  hero  is  represented  by  m'  K  .     The  summit  of 

\.  \  tor  tlu:n  t 

w'.     Tho  pressure  of  the  oohunn  A  K  bring  ^r«»atcr  than  Una 


(HAP.    IV.  WAVi;s.  45 

of;;/.'  K',  tho  point,  A  has  a  tendency  to  full,  niul  the  point  m7  to 

rise  by  reason  ol'  this  excess  oi'  pressure.  Therefore  in'  will 
rise  to  ti.e.  point  A',  while  A  sinks  to  tic-  level  in.  Tims  the 
points  A  iuid  in'  have  intercham'vd  levels;  the  point  m'  I>«MII»- 
now  raised  U>  IA  great  :i  hei'Mit  :ihove  the  Imttom  L  INI  as  the 
point  A  h:i«l  before  the  change,  Mini  the  point  A  having  fallen 
to  the  bright  whirl:  m'  hid.  In  like  manner  it  will  he  round 
th;:l,  lor  every  point  in  the  first  posilion  of  the  wave,  there  is 
another  point  in  the  second  position  with  whirh  it,  intercliam-r.; 
ulevations.  If  theae  circmiraances  he  elosely  considered,  it 
will  nol  he  di'.licnlt  to  perceive  that,  in  the  interval  which  we 
h:ue  supposed.  Hie  v.irioe.s  points  on  the  surface  of  the  w;i(er, 
such  :•  :  in',  winch  were  helore  on  the  sloping  sides  of  the  waves, 
have  i;o\v  hecoine  their  summits,  A'  !>'  (  •',  A  c.  Not  that  the 
points  A  IJC,  \T.  have  advanced  to  A'  15'  < '',  «S.  c.,  hut  that  they 
ha\e  1'allrn  iVoin  t.heir  former  elevations,  while  the  latter  have 
risen.  It  appears,  therefore,  that  the  undulations  of  the  sur- 
face are  produced  by  its  ditlerent  points  ascending  and  descend- 
ing r1!.. T.:.it,:dy  in  a '  perpcndicnlar  direction,  witliout  any  kind 
of  progressive,  motion. 

To  make  this  still  umro  clear, lot  us  aupi)ose  that  perpendicu- 
lar lines  he  drawn  from  every  part  of  the  surface  AaB&Cc, 
&C.totfce  coire.spondinn-  points  in  the  surface  A'  a'  B'  V  C'  c', 
v.id  let  the  interval  between  the  periods  at  which  the  sur- 

f  the  liijuid  assumes  these  two  forms  be  conceived  to  bij 
one  se. -OIK!  ;  in  that  time  the  several  points  of  the  first  surface, 
A\  !iic!i  are  marked  by  the  letters  /J,'fall  in  the  direction  of  the 
l  lines  perpendicularly  downwards  to  the  points  mark'-d 
//,  ;n: .!  tin-  jittini  :  marked  </  rise  perpendicularly  upwards,  in  tho 
directions  markiMl  by  the  dotted  lines,  to  the  positions  indicated 
bv  the  letters  ,/.  'Helween  the  two  positions  A  and  A',  the 
points  of  the  BUrfaCO  betWtJCXl  A  and  m'  have  both  risen  and 
fallen  during  tin-  B^concl  ;  they  hav6  fir:;t  risen  to  an  elevation 
<M|ii;il  to  that  of  A,  and  have  for  an  instant  in  their  turn  formed 
the  crest  of  the  wave  ;  but,  before  the  expiration  of  the  second, 
have  ji#uin  fallen  perpendicularly  to  their  position  in  the  dotted 
'  .  It  will  thin,  it  is  hoped,  be  understood  how  the /om  of  a 
wave  may  actually  have  a  progressive  motion,  while  the  water 
which  composes  it  is  stationary. 

I  f  :i  cloth  bo  loosely  laid  over  a  number  of  parallel  rollers  at 
s:icl,  a  distance  asunder  an  to  allow  the  cloth  to  full  between 
them,  the  shape  of  waves  will  be  exhibited.  If  a  progressive 
m. ii ion  he  nov,  given  t  >  the  rollers,  the  cloth  being  kept  sta- 
iionarv,  the  progressive  motion  of  waves  will  be  produced, — 
the  cloth  will  appear  to  advance.* 

if -i  ropOtlyini  itraigUl  >>n  -.-,  floor,  have  mio  of  its  emln  olovatod,  and  then 
Mi.i.ii-niv  iic;i',  Jar  Illusion  \\iii  be  |M...in,-,.,i,  <m  a  ilmilar  prinolple. 

K;-|)it;it«il  j:«rhy  euuxu  u  mu-ci^iioii  of  undulatloni. — AM.  Ke.         % 


A    TREATISE    ON    HYDROSTATICS.          CHAP.    IV. 

It  is  the  same  cause  which  makes  a  revolving  cork-screw, 
held  in  a  fixed  position,  seem  to  be  advancing  in  that  direction, 
in  which  it  would  actually  advance  if  the  worm  were  passing 
through  a  cork.  That  point  which  is  nearest  to  the  eye,  and 
which  corresponds  to  the  crest  of  the  wave  in  the  former  ex- 
ample, continually  occupies  a  different  point  of  the  worm,  and 
continually  advances  towards  its  extremity. 

This  property  has  lately  been  prettily  applied  in  ornamental 
clocks.  A  piece  of  glass,  twisted  so  that  its  surface  acquires  a 
ridge  in  the  form  of  a  screw,  is  inserted  in  the  mouth  of  some 
figure  designed  to  represent  a  fountain.  One  end  of  the  glass 
is  attached  to  the  axle  of  a  wheel  which  the  clockwork  keeps 
in  a  state  of  constant  rotation,  and  the  other  end  is  concealed 
in  a  vessel  designed  to  represent  a  reservoir  or  basin.  The 
continual  rotation  of  the  twisted  glass  produces  the  appearance 
of  a  progressive  motion,  as  already  explained,  and  a  stream  of 
water  continually  appears  to  flow  from  the  fountain  into  the 
basin. 

(41.)  The  properties  in  virtue  of  which  liquids  maintain  their 
level,  and  transmit  pressure,  are  the  cause  of  most  of  the  phe- 
nomena exhibited  in  the  various  motions  and  changes  to  which 
water  is  subject  on  the  surface  of  the  earth.  The  rain  which 
falls  on  the  tops  of  mountains  and  other  elevated  places,  if  it 
encounter  a  soil  not  easily  penetrable  by  water,  collects  in  rills 
and  small  drains,  which,  soon  uniting,  form  streams  and  rivulets. 
These,  descending  along  the  sides  of  the  elevations,  seeking  a 
lower  level,  gradually  encounter  others,  with  which  they  unite, 
and  at  length  swell  into  a  river.  The  waters,  still  having  a  ten- 
dency to  descend,  are  governed  in  their  course  by  the"  slopes 
of  the  ground  over  which  they  have  to  pass.  They  usually 
proceed  in  a  winding  channel,  directed  by  the  varying  form  of 
the  surface  of  the  country,  always  taking  that  course  which 
most  accelerates  their  descent.  "Sometimes  they  widen  and 
spread  into  a  spacious  area,  which,  losing  the  character  of  a 
river,  is  denominated  a  lake ;  again  contracting,  they  resume 
their  former  character  ;  and  after  being  swelled  and  increased 
by  tributary  streams,  they  at  length  come  to  their  final  destina- 
tion, and  restore  to  the  ocean  those  waters  which  had  originally 
been  taken  from  it  by  evaporation.  Throughout  the  whole  of 
this  process  the  only  principle  in  operation  is  the  tendency  of 
liquid  to  find  its  level. 

In  some  cases,  the  rain  which  is  lodged  on  elevated  grounds 
meets  a  soil  of  a  spongy  and  porous  nature,  or  one  which  by 
various  crevices  and  interstices  is  pervious  by  water.  In  such 
cases  the  liquid  often  passes  to  very  great  depths  before  it  en- 
counters a  barrier  formed  by  an  impenetrable  stratum.  When 
it  does,  and  is  confined,  it  is  subject  to  a  considerable  hydro- 


CHAP.    IV.  RITER8.  47 

static  pressure  from  the  water  which  fills  the  more  elevated 
veins  and  channels  by  which  it  is  fed.  This  pressure  frequent- 
ly forces  the  water  to  break  a  passage  through  the  surface,  and 
it  gushes  out  in  a  spring,  which  ultimately  enlarges  into  a  trib- 
utary stream  of  some  river.  In  some  cases,  the  water  which 
is  filtered  through  the  earth  is  confined  by  impenetrable  barriers 
in  subterraneous  reservoirs  ;  barriers,  the  strength  of  which 
exceeds  the  hydrostatic  pressure.  If  the  ground  perpendicu- 
larly above  such  a  barrier  be  opened,  and  a  pit  sunk  to  such  a 
depth  as  will  penetrate  those  strata  of  the  earth  which  are  im- 
pervious to  water,  the  liquid  in  the  subterraneous  reservoir, 
having  then  free  admission  to  the  pit,  will  rise  in  it  until  it  at- 
tain the  level  which  it  has  in  the  channels  from  which  it  is  sup- 
plied. If  this  level  be  above  the  surface  of  the  ground,  it  will 
have  a  tendency  to  rush  upwards,  and  if  restrained  by  proper 
means,  may  be  formed  into  a  fountain,  from  which  water  will 
always  flow  by  simply  opening  a  valve  or  cock.  If  the  level 
of  the  source  be  nearly  equal  to  that  of  the  mouth  of  the  pit,  the 
water  will  rise  to  that  level,  and  there  stand :  it  will  form  a  well. 
If  the  level  of  the  source  be  considerably  below  the  mouth  of 
the  pit,  the  water  will  not  rise  in  the  pit  beyond  a  certain 
height  corresponding  to  the  level  of  its  source.  In  this  case,  a 
pump  is  introduced  into  the  pit,  and  the  water  is  raised  upon 
principles  which  will  be  explained  when  we  come  to  treat  of 
pneumatics. 

The  water  collected  in  the  earth  in  this  manner  by  infiltra- 
tion, sometimes  bursts  its  bounds  and  rushes  into  the  bed  of 
the  sea.  It  is  stated  by  Humboldt,  that  at  the  mouth  of  the 
Rio  los  Gartos  there  are  numerous  springs  of  fresh  water  at  the 
distance  of  500  yards  from  the  shore.  Instances  of  a  similar 
kind  occur  in  Burlington  bay  on  the  coast  of  Yorkshire,  in 
Xagua  in  the  island  of  Cuba,  and  elsewhere. 

Those  sublime  natural  objects,  cataracts  and  waterfalls,  are 
manifestations  of  the  tendency  of  liquids  to  maintain  their  level. 
Whftn  by  the  union  of  streams  large  quantities  of  water  are 
collected  at  elevations  considerably  raised  above  the  level  of 
the  sea,  the  river  whose  head  is  thus  formed  frequently  encoun- 
ters, in  its  approach  to  the  sea,  abrupt  declivities,  down  which 
it  is  precipitated  in  a  cataract.  The  heights  of  the  cataracts 
of  the  great  rivers  of  the  world,  though  commonly  much  exag- 
gerated, are  still  such  as  to  place  these  tremendous  phenomena 
among  the  most  appalling  of  natural  appearances.  The  cele- 
brated cataract  of  TEQCENDAMA,  formed  by  the  Rio  Bogota,  in 
South  America,  was  long  considered  to  be  the  highest  in  the 
world,  the  fall  having  been  estimated  by  Bouguer  to  be  not  less 
than  1500  perpendicular  feet.  Humboldt,  however,  has  more 
recently  found  this  calculation  to  bo  erroneous,  and  has  shown 


43  A    TREATISE    ON    HYDROSTATICS.  CHAP.    IV. 

that  the  Height  of  the  fall  does  not  exceed  600  feet*  The 
stream  before  it  approaches  the  precipice  has  a  breadth  of  140 
feet,  .which  immediately  contracts,  and  at  the  edge  of  the  abyss 
is  reduced  to  35  feet.  The  great  cataracts  of  Niagara  are  well 
known ;  the  breadth  of  the  stream  is  400  yards  immediately 
before  the  descent,  and  the  liquid  is  precipitated  through  the 
perpendicular  height  of  150  feet.  The  sound  of  this  cataract 
is  distinctly  audible  at  a  distance  of  thirteen  miles. 

The  motion  of  water  in  rivers  has  a  sensible  effect  in  wear- 
ing away  their  beds.  By  this  means,  in  the  course  of  time,  the 
face  of  a  country  may  undergo  considerable  changes.  The 
falls  of  Niagara  are  gradually  changing  their  aspect  by  this 
cause  ;  and  it  is  probable  that  a  period  will  come,  when  the  bed 
of  the  stream  between  these  falls  and  Lake  Erie  will  be  worn 
to  a  depth  such  as  to  drain  the  entire  of  the  waters  of  that  in- 
land sea,  and  convert  the  space  it  now  occupies  into  a  fertile 
plain.f  Such  a  change  appears  to  have  been  already  produced 
at  the  falls  of  the  Nile  at  Syene,  which  are  not  at  all  conforma- 
ble to  what  we  learn  from  the  ancients  to  have  existed  there  in 
former  times. 

In  accomplishing  their  descent  to  the  level  of  the  ocean, 
rivers  sometimes  suddenly  disappear,  finding  through  subterra- 
nean caverns  and  channels  a  more  precipitate  course  than  any 
which  the  surface  offers.  After  passing  for  a  certain  space 
thus  under  ground,  they  reappear,  and  flow  in  a  channel  on  the 
surface  to  the  sea.  Sometimes  their  subterraneous  passage 
becomes  choked,  and  they  are  again  forced  to  find  a  channel 
on  the  surface.  The  waters  of  the  Oronoko  lose  themselves 
beneath  immense  blocks  of  granite  at  the  Randal  de'  Cariven, 
which,  leaning  against  one  another,  form  great  natural  arches, 
under  which  the  torrent  rushes  with  immense  fury.  The 
Rhone  disappears  between  Seyssel  and  Sluys.  In  the  year 
1752,  the  bed  of  the  Rio  del  Norte,  in  New  Mexico,  became 
suddenly  dry  to  the  extent  of  60  leagues  ;  the  river  had  pre- 
cipitated itself  into  a  newly  formed  chasm,  and  disappeared  for 
a  considerable  time,  leaving  the  fine  plains  upon  its  banks  en- 
tirely destitute  of  water.  At  length,  after  a  lapse  of  several 
weeks,  the  subterraneous  channel  having  apparently  become 
choked,  the  river  returned  to  its  former  bed.  A  similar  phe- 
nomenon is  said  to  have  occurred  in  the  river  Amazon,  about 
the  beginning  of  the  eighteenth  century.  At  the  village  of 
Puyaya,  the  bed  of  that  vast  river  was  suddenly  and  completely 
dried  up,  and  remained  so  for  several  hours,  in  consequence  of 
part  of  the  rocks  near  the  cataract  of  Rentena  having  been 
thrown  down  by  an  earthquake.^ 

*  Humboldt's  Researches,  vol.  i.  p.  76. 

(•  Brewster'a  Edinburgh  Encyclopedia,  vol.  xvi.  p.  519. 

t  Brewster's  Edinburgh  Encyc.  vol.  xvi.  p.  519.     Humboldt,  vol.  ii.  p.  312. 


CHAP.    IV. 


CANALS. 


49 


(42.)  The  methods  of  conducting  a  canal  through  a  country 
depend  upon  this  property,  by  which  liquids  find  their  level : 
when  the  space  through  which  the  canal  is  to  be  conducted  is 
not  a  uniform  level  plain,  the  effects  of  its  declivity  are  provid- 
ed against  by  contrivances  called  locks.  If  a  canal  were  cut 
upon  an  inclined  surface,  the  water  would  run  towards  the  lower 
extremity, 'and  overflow  the  bank,  leaving  the  higher  end  dry. 
A  channel  of  any  considerable  length,  even  with  a  gentle  and 
gradual  slope,  would  be  attended  with  this  effect. 

The  course  of  the  canal  is  therefore  divided  into  levels  of 
various  lengths,  according  to  the  inequalities  of  the  country 
through  which  it  passes.  Let  A  B,  Jig.  30.,  represent  a  slope, 

Pig.  30. 


along  which  it  is  required  to  conduct  a  canal.  A  series  of  lev" 
els,  A  D,  E  F,  G  B,  are  constructed  artificially,  partly  by  form- 
ing mounds,  L  E  K  and  M  G  B,  and  partly  by  excavations, 
A  D  L  and  K  F  M.  The  canal  is  carried  successively  along 
each  of  the  levels  B  G,  F  E,  DA.  These  communicate  with 
each  other  by  locks  at  E  D  and  G  F,  by  means  of  which  vessels 
passing  in  either  direction  are  raised  or  lowered  with  perfect 
ease  and  safety. 

The  construction  of  a  lock  is  easily  understood.     Let  A  B 
and  G  D,  Jig.  31.,  be  two  adjacent  levels  of  a  canal ;  the  water 

Fig.  31. 

~          A 


in  the  higher  level  A  B,  is  confined  by  a  floodgate,  B  C,  which 
may  be  opened  and  closed  at  pleasure,  and  near  the  bottom  of 
which  are  small  openings,  covered  by  sliding  boards,  through 
which  water  in  the  higher  level  may  be  allowed  gradually  to 
flow  into  the  lower  one.  Suppose  C  E  a  length  sufficient  to 
contain  the  vessels  which  are  to  pass  the  lock ;  at  E  let  another 
floodgate  be  placed,  carried  to  a  height  equal  to  the  level  of 
the  water  in  A  B.  If  a  vessel  is  to  be  passed  from  the  higher 
level  to  the  lower,  the  floodgate  F  G  is  closed,  and  the  sluice* 


A    TREATISE    ON    HYDROSTATICS.  CHAP.    IV, 


fnV^0^  *f  n  C  T  °pened'     The  water  flows  from  these 
into  the  lock  BG  and  continues  to  flow  until  it  attains  the 

ed    anl  Ih    '"        l     ^  and  ^  A  R     The  *ate  B  C  1S  then  °Pen- 
ed  and  the  vessel  is  drawn  from  A  B  into  the  lock.     The  crate 

is  then  closed,  and  the  sluices  at  the  bottom  of  F  G^are 
opened.  The  water  begins  to  flow  from  the  lock  into  E  D,  and 
the  level  of  the  water  in  the  lock  gradually  subsides.  The 
vessel  floating  upon  it  is  thus  slowly  lowered  ;  and  this  con- 
tinues until  the  water  in  the  lock  attains  the  same  level  as  the 
water  in  E  D  The  gate  F  G  is  then  opened,  and  the  vessel  is 
drawn  out  of  the  lock  into  the  lower  level. 

A  vessel  is  conducted  from  the  lower  to  the  higher  level  bv 

le  reverse  of  this  process.     The  gate  B  C  being  closed,  and 

the  gate  F  G  opened,  the  water  in  the  lock  and  m  E  D  stands 

at  the  same  level.     The  vessel  is  drawn  into  the  lock,  and  the 

gate  F  G  closed.     The  sluices  in  B  C  are  opened,  and  water 

permitted  to  pass  gradually  from  the  higher  level  into  the  lock  ; 

the  surface  of  the  water  in  the  lock  is  thus  slowly  elevated 

raising  the  vessel  with  it  ;  and  this  continues  until  its  surface 

Attain  the  level  of  the  water  in  AB.     The  gate  BC  is  then 

opened,  and  the  vessel  drawn  into  the  higher  level 

In  whichever  direction  a  vessel  pass  through  a  lock,  it  is  evi- 

dent that  a  quantity  of  water  sufficient  to  raise  the  level  of  the 

water  m  the  lock  to  that  of  the  higher  level  must  pass  from  the 

higher  to  the  lower  level  ;  the  canal  must,  therefore,  be  always 

led  with  a  sufficient  quantity  of  water  to  supply  this  waste.* 

ie  objections  to  locks  are  the  delay  they  occasion  and  the  ex- 

their  construction,  their  repairs,  and  their  attendance. 

the  £ofCendil?f  ,b°at3  "-Cr  requir°  a  quai>t'ty  of  water,  which,  independently  of 
level  norT+lt  reclul8lte  J°  raise  the  surface  of  the  water  to'that  of  the  higher 
scendin"  l™t?  quantity  required  to  pass,  in  the  case  of  ascending  and  de- 

lock  thf  bSftomnofrwr  T  '      ?"mm**»™*?'    When  a  descending  boat'enters  a 


tn  '„  ,'.  no      e  par    o   the  lower  level,  behind  it,  a  por- 

tion of  water  equal  to  the  immersed  part  of  the  boat;  and  the  gates  bein-  closed 
elnnd  it,  a  quantity  of  water  is  required  to  pass  into  the  lock  from  the  uppe°r  level 
°  C  PaC'l    ° 


i  i  r  ,          Part,  °f  the  Iock>  situated  ^tween  the  upper  and 

lower  levels,  diminished  by  the  bulk  of  the  immersed  part  of  the  boat  •  and  this 
last  being  the  quantity  forced  out  by  the  boat  on  entering,  it  is  evident/that  with 


on  entering,  it  is  evidentthat  with 
s  of  as- 
d 

the 


eaviy  aen     e    oat,  an    the  more  exact  its  adaptation  to  the  lock, 
fftina  ti     i6  (:xpfondltu1re-     Thc  foregoing  considerations  would  be  useful  for  regu! 
ting  the  heights,  and  consequently  the  number  of  locks,  the  forms  of  their  hot- 
m^ianieni  Y1d  l1^  rclatlV,0  t0nnaSe'  °"  Ascending  and  descending,  large  and 
small,  and  loaded  and  empty  boats.     This  i,  not  the  place  for  more  minute  d«H 


CHAP.    IV.  SUPPLY    OF    WATER    FOR   TOWNS.  51 

It  is  therefore  often  better,  where  it  can  be  accomplished,  to 
carry  the  canal  through  a  circuitous  course,  than  to  take  a 
shorter  route  with  a  greater  number  of  locks. 

Owing  to  the  small  quantity  of  friction  which  exists  between 
the  particles  of  a  liquid  and  a  solid,  the  slightest  inclination  in 
the  channel  is  sufficient  to  cause  the  water  to  flow.  In  a 
straight  and  smooth  channel  a  descent  of  one  foot  in  about 
four  miles  will  cause  the  stream  to  flow  at  the  rate  of  three 
miles  an  hour.  The  average  slope  of  the  principal  rivers  of 
the  world  is,  however,  greater  than  this. 

(43.)  It  is  necessary  at  all  times  to  know  the  level  of  the 
water  in  the  boiler  of  a  steam  engine  ;  but  that  being  a  close 
vessel  formed  of  metal,  it  is  impossible  by  any  external  indica- 
tion to  perceive  the  water  within.  A  glass  tube,  A  B,  Jig.  32., 

Fig.  32. 

»        -'  "**!   C"    .' 


is  inserted  in  the  side  of  the  boiler ;  one  end,  A,  passes  into 
the  boiler  near  the  top,  and  the  other  end,  B,  near  the  bottom. 
The  water  in  this  tube  must  always  stand  at  the  same  level 
with  the  water  of  the  boiler ;  arid  the  tube  being  of  glass,  this 
level  may  always  be  observed.  The  indication  of  the  tube 
would  not  in  this  case  be  correct,  if  the  upper  end  A  were  not 
inserted  in  the  boiler,  but  left  open  to  the  atmosphere.  The 
surface  of  the  water  in  the  boiler  is  subject  to  the  pressure  of 
the  steam,  which  is  there  confined  ;  and  in  order  that  the  sur- 
face of  the  water  in  the  tube  should  have  the  same  level,  it 
must  be  subject  to  the  same  pressure.  This  will  necessarily 
be  the  case,  if  the  top  of  the  tube  communicate  with  the  steam 
by  being  inserted  in  the  boiler  at  A. 

(44.)  The  method  of  supplying  water  for  towns  depends  on 
the  property  of  maintaining  its  level ;  a  reservoir  is  selected  in 
some  situation  more  elevated  than  those  places  to  which  the 
water  is  to  be  supplied.  This  reservoir  is  fed  either  from  nat- 
ural sources  or  by  mechanical  power.  Pipes  are  conducted 
from  it,  usually  under  ground,  through  all  parts  of  the  town  ; 
and  from  the  main  pipes  smaller  ones  ramify,  and  pass  into 
each  house.  These  pipes  may  be  carried  in  any  direction 
which  may  be  desirable,  and  alternately  up  and  down  the  steep- 


53  A    TREATISE    ON   HYDROSTATICS.  CHAP.    IV. 

est  hills,  and  to  the  tops  of  the  highest  houses,  providing  that 
the  level  of  the  water  in  the  reservoir  be  above  the  highest 
points  to  which  the  pipes  are  carried. 

By  such  means  a  constant  and  abundant  supply  of  water  for 
domestic  purposes  may  be  introduced  into  the  upper  apart- 
ments, and  when  used  may  be  carried  off  by  waste  pipes 

Ignorance  of  this  principle,  by  which  liquids  return  to'  their 
level,  is  shown  m  the  construction  of  aqueducts  by  the  ancient' 
for  supplying  water  to  towns.  If  it  were  requisite  to  conduct 
water  across  a  valley,  a  bridge  was  constructed  on  arches,  sup- 
porting a  canal  through  which  the  water  was  carried.  A  pipe 
conducted  under  ground  across  the  valley  would  have  served 
tne  same  end,  with  far  less  expense  ;  for  the  water  would  rise 

other     m        P1PG  °n  thC  °ne  Slde  aS  it:  had  descended  on  the 
(45.)  Taken  in  a  loose  popular  sense,  the  term  "level"  is 
easily  comprehended  ;  it  is  necessary  here,  however,  to  explain 
its  import  more  exactly.     The  figure  of  the  earth  is  that  of  a 
globe,  or  nearly  so  ;  there  are  inequalities  on  its  surface,  but 
they  are  so  insignificant,  that,  when  compared  with  its  own 
magnitude,  the  most  enormous  mountains  resemble  impercepti- 
le  particles  of  dust,  resting  on  those  globes  which  are  used  to 
represent  the  earth,  and  on  which  its  natural  and  Apolitical  di- 
visions are  depicted.     These  inequalities,  small  as  thev  are 
cease  to  exist  on  the  surface  of  the  waters  when  thev  are  not 
agitated    by  wind.      They  present,  in   that  case,  a  surface 
uniformly  curved,  and  which,  if  continued  in  every  direction 
without  mterruption  would  assume  that  figure  which  is  ascribed 
>  the  earth.     If  a  line  be  drawn  from  the  centre  of  the  earth 
to  any  part  of  this  surface,  that  line  will  represent  the  direction 
in  which  the  attraction  of  gravity  acts.     It  will  be  the  direction 
Fig.  33.      in  which  a  plumb-line  will  hang  when  at  rest  •  and 
/;;-  -V%X    <<he  surface  of  the  earth,  such  as  it  has  been'  just 
"~         descnbed>  wil1  be  every  where  perpendicular  to 
;  lines  thus  drawn.*     Below  and  above  the  actual 
!  surface  of  the  earth,  other  concentrical  surfaces 
may  be  conceived,  as  represented  mfig.  33.  by  the 
dotted  circles.     Each  of  these  surfaces  will  enjoy 


to  the  surface,  unless  the  earth  were  a  perfect  globe,  or  sphere 
'  ""    C  P 


fetaf       '!      -     t  h  T        S          '  "  n0t  Ciefly  ow»*  ^its  moiains,  thef 
feet  [of  which  might  be  here  neglected,  but  to  its  oblateness,  or  its  being  flattened 
at  the  poles,  and  protuberant  at  the  equator.    Many  instances  occur  il  the  text 
™    cle,ntlfic  Precision  would  require  the  use  of  «  vertical  » 

has  beefl  employed'  to  avoid  the  a-*-*  «• 


CHAP.  IV.        SURFACE  OF  SEA  CURBED.  53 

the  same  properties  as  have  been  already  ascribed  to  the  sur- 
face of  the  earth.  Each  of  them  will  be  every  where  perpen- 
dicular to  straight  lines  diverging  from  the  centre,  and  will  ba 
every  where  equally  distant  from  that  point. 

Every  part  of  each  of  these  concentrical  surfaces  is  said  to 
form  the  "  same  level ;"  and  one  level  is  said  to  be  "  above"  or 
"  below"  another  level,  according  as  it  is  more  or  less  distant 
from  the  centre.* 

When  a  liquid  mass  placed  upon  the  earth  is  quiescent,  eve- 
ry part  of  its  surface  settles  itself  in  the  same  level,  and  all 
parts  which  are  disposed  in  any  other  level  under  its  surface 
are  subject  to  tiie  same  pressure  ;  that  pressure  being  great 
in  proportion  to  the  depth  of  the  level  in  question  below  the 
surface. 

(46.)  Notwithstanding  the  globular  form  of  the  earth,  a  sheet 
of  water  on  a  calm  day  appears  to  exhibit  a  plane  surface,  no 
curvature  whatever  being  perceivable.  The  cause  of  this  is 
easily  discovered  in  the  small  proportion  which  such  a  surface 
bears  to  the  whole  earth.  Let  us  suppose  a  circular  lake  of 
four  miles  in  diameter,  and  conceive  a  straight  line  to  be  drawn, 
or  a  cord  stretched  across  it,  between  two  opposite  points.  By 
reason  of  the  curvature  of  the  surface,  this  cord  would  be  under 
the  water  towards  the  middle,  if  it  only  touched  the  water  at 
the  extremities ;  and  its  depth  would  be  greatest  at  the  centre 
of  the  lake.  Nevertheless,  in  the  case  we  have  supposed,  its 
depth  at  that  point  would  only  be  15|  inches  ;  the  curvature, 
therefore,  in  a  circuit  of  two  miles  round  a  given  point,  will  not 
raise  that  point  16  inches  above  the  plane  surface,  passing 
through  the  extreme  points  of  the  circuit. 

It  is  not  wonderful,  then,  if  fluid  surfaces  of  small  extent 
appear  to  be,  and  practically  speaking  really  are,  plane,  the  de- 
gree of  curvature  being  insignificant.  Any  plane  surface  of  a 
small  extent  is,  then,  said  to  be  level,  when  it  is  parallel  to  the 
surface  of  a  liquid  which  is  quiescent ;  and  all  particles  of  a 
liquid  which  are  disposed  in  the  same  plane,  parallel  to  its  sur- 
face, are  said  to  be  in  the  same  level. 

Although,  as  we  have  just  stated,  the  curvature  of  the  surface 
of  a  liquid  be  very  small,  yet,  if  that  surface  have  sufficient  ex- 
tent, the  curvature  may  be  ascertained  by  observation.  When 
a  distant  vessel  first  comes  within  sight  at  sea,  the  point  of  the 
mast  only  is  perceived ;  as  it  approaches  the  mast  gradually 
rises  ;  and  last  of  all  appears  the  hulk,  which,  from  its  magni- 
tude, would  be  the  first  seen,  if  the  swelling  curve  of  the  sur- 
face of  the  sea  had  not  obstructed  the  view  of  it. 

(47.)  The  law,  by  which  all  parts  of  the  surface  of  the  same 

*  The  concentrical  surfaces  are  expressed  in  French  authors  by  the  term 
"  couches  do  nivean." 


54 


A    TREATISE    ON    HYDROSTATICS. 


CHAP.    IV. 


liquid  rest  in  the  same  level,  will  not  be  violated  if  one  liquid 
be  placed  upon  another,  or  even  if  a  series  of  liquids  were 
placed  one  above  another.  If  a  glass  vessel, /g-.  34.,  be  partly 

Fig.  34. 


filled  with  water,  W,  and  on  the  water,  oil,  O,  be  poured,  the 
surface  of  the  water  will  continue  to  be  level,  bearing  the  oil 
upon  it.  Again,  if  another  liquid,  as  ether,  E,  be  poured  upon 
the  oil,  the  surface  of  the  oil  on  which  the  ether  rests  will  con- 
tinue to  be  level ;  and  so  on.  In  these  cases,  however,  the 
pressure  of  the  liquids  on  any  stratum  is  not  proportional  to  the 
depth  of  the  stratum.  The  pressure  at  any  level  is  equal  to  the 
weight  of  the  incumbent  column  of  liquid.  But  that  column 
is  not,  as  in  the  cases  formerly  considered,  composed  of  the 
same  liquid,  and,  therefore,  it  is  not  true  that  any  part  of  the 
column  has  a  proportional  weight. 

The  various  appearances  produced  in  ornamental  water- 
works are  the  effects  of  pressure  transmitted  through  pipes 
from  a  head  of  water,  considerably  raised  above  the  orifices 
from  which  the  water  is  required  to  be  projected.  The  form 
and  direction  of  these  orifices  determine  the  figure  which  the 
jet  or  fountain  will  assume  ;  and  the  height  of  the  water  trans- 
mitting the  pressure  will  determine  the  altitude  to  which  the 
water  of  the  fountain  will  be  projected. 

(48.)  Instruments  for  leveling  or  determining  the  direction 
or  position  of  horizontal  lines,  or  the  relation  between  the  lev- 
els in  which  different  objects  are  placed,  are  constructed  by 
means  of  the  property  by  which  liquids  maintain  their  level. 
Let  A,  Jig.  35.,  be  a  straight  glass  tube,  having  two  ether  glass 
tubes,  B  and  C,  united  with  it  at  right  angles.  Let  the  tube  A, 
and  a  part  of  each  leg  B  and  C,  be  filled  with  a  liquid,  the  legs 
B  and  C  being  presented  upwards.  On  the  surfaces  a  b  of  the 
liquid  in  the  legs,  let  floats  be  placed,  carrying  upright  wires,  to 
the  ends  of  which  are  attached  sights,  S  T,  consisting  of  two 
fine  threads  or  hairs  stretched  at  right  angles  across  a  square  : 


CHAP.    IT. 


LEVELING. 


these  sights  are  placed  at  right  angles  to  the  length  of  the  in- 
strument, and  a  front  view  of  them  is  represented  at  S'  T;;  and 
they  should  be  so  adjusted  that  the  points  where  the  hairs  in- 
tersect shall  he  at  equal  heights  above  the  floats.  This  ad- 
justment may  be  made  in  the  following  manner : — 

Let  the  eye  be  placed  behind  one  of  the  sights,  looking 
through  it  at  the  other,  so  as  to  make  the  points  where  the  hairs 
intersect  cover  each  other,  and  let  some  distant  object  covered 
by  this  point  be  observed.  Let  the  instrument  be  now  revers- 
ed, and  let  the  points  of  intersection  of  the  hairs  be  viewed  in 
the  same  way,  so  as  to  cover  each  other.  If  they  s,re  observed 
to  cover  the  same  distant  point  as  before,  they  will  be  equal 
heights  above  the  surfaces  of  the  liquid.  But  if  the  same  dis- 
tant point  be  not  observed  in  the  direction  of  these  points,  then 
one  or  the  other  of  the  sights  must  bo  raised  or  lowered,  by  an 
adjustment  provided  for  that  purpose,  until  the  points  of  inter- 
section be  brought  into  that  direction.  These  points  will  then 
be  properly  adjusted,  and  the  line  passing  through  them  will  be 
truly  horizontal.  All  points  seen  in  the  direction  of  the  sights 
will  then  be  in  the  level  of  the  instrument. 

The  principles  on  which  this  adjustment  depends  are  easily 
explained :  if  the  intersection  of  the  hairs  be  at  the  same  dis- 
tance from  the  floats,  the  line  joining  those  intersections  will 
evidently  be  parallel  to  the  lines  joining  the  surfaces  a  b  of  the 
liquid,  and  will,  therefore,  be  level.  But  if  one  of  these  points 


56  A  TREATISE  ON  HYDROSTATICS.  CHAP.  IV. 

be  more  distant  from  the  floats  than  the  ether,  the  line  joining 
the  intersections  will  point  upwards  if  viewed  from  the  lower 
sight,  and  downwards  if  viewed  from  the  higher  one.  On  re- 
versing the  instrument  this  line  must  take  a  different  direction, 
and  therefore  will  not  be  presented  to  the  same  object. 

The  accuracy  of  the  results  given  by  this  instrument  may  be 
increased  to  any  extent,  by  lengthening  the  tube  A. 

(49.)  Another  instrument  for  leveling  is  known  by  the  name 
of  the  spirit  level:  it  consists  of  a  cylindrical  glass  tube  filled 
with  spirits  of  wine,  except  a  small  space  which  is  occupied  by 
air ;  the  ends  are  hermetically  sealed,  to  prevent  the  escape  of 
the  fluid.  In  whatever  position  the  tube  be  placed,  the  liquid 
will  always  tend  to  the  lowest  part  of  it ;  if  either  end  be  raised 
above  the  other,  at  that  extremity  will  the  bubble  of  air  be  found, 
the  liquid  having  retired  to  the  other.  If  the  extremities  be  at 
the  same  level,  the  bubble  of  air  will  settle  at  the  highest  inter- 
mediate point.  The  tube  is  not  strictly  straight,  but  is  slightly 
curved,  the  convexity  being  presented  upwards.  Whatever  be 
the  position  of  the  tube,  the  air  bubble  will  rest  at  the  highest 
x)oint  of  the  curve  ;  and  if  the  extremities  be  at  the  same  height, 
this  will  be  the  middle  point.  The  tube  in  a  horizontal  position, 
with  the  air  bubble  resting  in  the  centre,  is  represented  in 
fig.  36. 

Fig.  36. 


The  method  of  mounting  the  level  for  the  pui  pose  of  fixing 
a  plane  in  a  horizontal  position,  is  commonly  to  fix  the  tube  in 
a  block  of  wood,  or  in  a  case  of  brass,  A  B,J%.  37.  The  block 
is  fixed  in  such  a  position,  that  when  the  lowest  surface,  D  E, 
is  horizontal,  the  bubble  will  stand  in  the  centre  between  two 
lines,  a  and  &,  cut  upon  the  tube.  The  instrument  may  be  ad- 
justed by  the  following  method : — Let  a  plane  surface  be  con- 
structed as  nearly  horizontal  as  possible,  and  let  the  surface 
D  E  be  placed  upon  it.  Let  the  tube  be  fixed  into  the  block  in 


CHAP.    IV.  SPIRIT    LEVEL.  57 

such  a  manner  that  the  bubble  will  stand  between  the  wires  a 
and  b  ;  this  being  accomplished,  let  the  instrument  be  now  re- 
versed, the  extremities  D  and  E  exchanging  places.  If  the 
bubble  stand  still  in  the  middle,  it  proves  the  instrument  to  be 
correct ;  if  not,  the  end  towards  which  it  retires  is  the  higher 
extremity.  The  bubble  must  then  be  brought  back  to  the  cen- 
tre, partly  by  lowering  the  extremity  of  the  tube  toward  which 
it  moves,  and  partly  by  adjusting  the  plane  surface  on  which 
the  instrument  is  placed.  The  instrument  must  now  be  once 
more  reversed,  and  the  same  process  repeated,  until  the  change 
of  position  of  the  instrument  no  longer  deranges  the  position 
of  the  bubble. 

The  principle  on  which  this  adjustment  depends,  is  that  the 
bubble  will  fix  itself  at  the  highest  point  of  the  tube,  and  that  a 
horizontal  line  is  at  right  angles  to  a  vertical  one.  When  by 
adjusting  the  tube  the  bubble  is  fixed  in  the  centre  of  the  wires 
a  and  6,  let  us  suppose  a  vertical  line,  c  </,  drawn  from  the  cen- 
tre of  the  bubble  to  meet  the  base,  D  E,  of  the  instrument.  If 
D  E  be  perpendicular  to  c  d,  it  is  apparent  that  reversing  the 
instrument  will  make  no  change  in  the  position  of  the  line 
c  d,  and  that  the  point  c  will  still  continue  to  be  the  place 
of-  the  bubble.  But  in  this  case  D  E  being  perpendicular  to  a 
vertical  line  must  be  horizontal.  If,  however,  D  E  be  not  per- 
pendicular to  c  <Z,  one  of  the  angles,  suppose  c  d  D,  will  be 
acute,  and  the  other,  c  d  E,  obtuse  ;  and,  therefore,  the  point  D 
will  be  more  elevated  than  the  point  E.  On  reversing  the  in- 
strument, E  will  take  the  more  elevated,  and  D  the  less  elevat- 
ed position.  The  middle  point,  c,  will  no  longer  be  the  highest 
point  of  the  tube,  and  accordingly  the  bubble  will  retire  from  it. 


68  A  TREATISE  ON  HYDROSTATICS.  CHAP.    V. 

CHAP.   V. 

^r 

OF  THE  IMMERSION  OF  SOLIDS  IN  LiaUIDS. 

TO  DETERMINE  THE  EXACT  MAGNITUDE  OF  AN  IRREGULAR  SOLID. — 
WHEN  SOLUBLE  IN  THE  LIQUID. — WHEN  POROUS. — EFFECT  ON  THE 
APPARENT  WEIGHT  OF  THE  LIQUID. — EFFECT  ON  THE  APPARENT 
WEIGHT  OF  THE  SOLID. — THE  REAL  WEIGHT  OF  THE  SOLID  AND 
LIQUID  NOT  CHANGED  BY  IMMERSION.— CAUSE  OF  THE  APPARENT 
CHANGE. — WHEN  A  BODY  IS  SUSPENDED. — FLOATING  BODIES.— 
THESE  PROPERTIES  DEDUCED  FROM  THE  FUNDAMENTAL  PRINCIPLES 
OF  HYDROSTATICS. — THE  SAME  SOLID  SINKS  IN  SOME  LIQUIDS  AND 
RISES  IN  OTHERS. — BUOYANCY.— ITS  EFFECTS  IN  SUBMARINE  OPERA- 
TIONS.— ITS  EFFECTS  PERCEIVABLE  IN  BATHING.— BOATS  MAY  BE 
FORMED  OF  ANY  MATERIAL,  HOWEVER  HEAVY. — AN  IRON  BOAT, 
WHICH  CANNOT  SINK.— METHOD  OF  PREVENTING  SHIPS  FROM  FOUN- 
DERING.—EFFECTS  OF  THE  CARGO.— BALL  COCK,  AND  OTHER  FLOAT- 
ING REGULATORS. — MEANS  OF  RAISING  WEIGHTS  FROM  THE  BOTTOM 
OF  THE  SEA. — METHOD  OF  LIFTING  VESSELS  OVER  SHOALS. — LIFE- 
PRESERVERS. — SWIMMING. — WATER  FOAVL. — FISH.— WHY  A  DROWN- 
ED BODY  FLOATS. — PHILOSOPHICAL  TOY. — WHY  ICE  FLOATS.— ROCKS 
RAISED  TO  THE  SURFACE  BY  ICE. 

(50.)  To  ascertain  by  direct  measurement  the  volume  or  size  of 
a  solid  body  is  a  problem  of  considerable  practical  difficulty,  ex- 
cept in  cases  where  the  body  has  some  regular  shape  or  figure  ; 
thus,  for  example,  if  it  were  required  to  determine  the  exact 
number  of  solid  inches  and  parts  of  a  solid  inch  in  a  rough  lump 
of  mineral  ore,  the  surfaces  of  which  present  numerous  and  ir- 
regular projections  and  cavities,  science  would  in  vain  furnish 
rules  for  calculating  the  volume  of  bodies  bounded  by  surfaces 
of  given  figures  and  magnitudes,  and  meeting  under  given  an- 
gles. The  exact  practical  solution  of  the  problem  by  direct 
geometrical  measurement  is  impossible. 

Bodies  in  the  liquid  form  do  not  present  the  same  difficulties ; 
their  peculiar  qualities  cause  them  to  adapt  themselves  with 
facility  to  any  form,  and,  without  undergoing  any  change  of 
magnitude,  to  take  the  figure  of  any  vessel  in  which  they  are 
placed.  Thus,  if  it  be  required  to  ascertain  the  number  of  cubic 
inches  in  a  mass  of  liquid,  let  a  perpendicular  vessel  be  taken, 
the  base  of  which  is  equal  to  a  cubic  inch,  and  let  the  liquid  be 
poured  into  this  vessel ;  so  much  of  the  liquid  as  fills  a  part  of 
this  vessel  one  inch  in  height  has  the  magnitude  of  one  cubic 
inch ;  so  much  as  fills  it  to  the  height  of  an  inch  and  a  half  has 
the  magnitude  of  a  cubic  inch  and  a  half;  and  so  on  for  other 
heights. 

This  great  facility  which  the  measurement  of  liquids  presents, 
and  the  difficulty,  on  the  other  hand,  which  attends  the  measure- 


CHAP.  V. 


MEASUREMENT  OF  SOLIDS. 


59 


ment  of  solids,  are  the  causes  why  the  quantity  of  bodies  in  the 
liquid  form  is  usually  expressed  by  their  measure,  while  the 
quantity  in  the  solid  form  is  commonly  expressed  by  their 
weight :  thus,  if  we  speak  of  a  liquid,  we  say  it  is  so  many 
hogsheads,  gallons,  quarts,  &c. ;  on  the  other  hand,  speaking 
of  a  solid,  we  say  it  is  so  many  tons,  hundreds,  pounds,  &c. 

(51.)  The  same  property  which  renders  the  volume  of  a  liquid 
easily  determined,  also  points  it  out  as  the  means  of  determin- 
ing the  dimensions  of  a  solid.  As  a  liquid  will  adapt  itself  to 
the  shape  of  the  vessel  which  contains  it,  filling  every  part  of 
that  vessel  below  its  own  level,  it  will  in  like  manner  adapt  it- 
self to  the  figure  of  any  solid  which  may  be  immersed  in  it;  so 
that  if  the  liquid  were  hardened  and  solidified,  and  the  solid 
withdrawn,  an  exact  mould  of  the  solid  would  be  exhibited  by 
the  hardened  liquid.  Such,  in  fact,  is  the  method  by  which  all 
moulds  are  made.  A  body  naturally  solid  is  liquefied  by  ex- 
posure to  heat,  or  by  moisture,  or  by  other  means.  The  solid, 
the  shape  of  which  is  to  be  taken,  is  then  immersed  in  it,  and 
the  liquid  is  hardened  either  by  cooling,  or  drying,  or  otherwise. 
The  body  is  then  withdrawn,  leaving  its  form  impressed  on  the 
substance  in  which  it  was  immersed. 

When  a  solid  is  thus  immersed  in  a  liquid,  it  displaces  a  quan- 
tity of  that  liquid  equal  in  size  to  that  part  of  the  solid  which  is 
immersed.  If,  therefore,  the  bulk  of  the  liquid  thus  displaced 
could  be  ascertained,  the  magnitude  of  the  part  of  the  body  im- 
mersed would  be  determined. 


This  is  easily  accomplished.  Let  A  B  C  D,  Jig.  38.,  be  «. 
vessel  containing  a  liquid,  which  we  will  suppose,  in  the  Gst 
instance,  stands  at  a  level,  E  F  ;  we  shall  suppose  also,  for  the 
present,  that  the  vessel  has  perpendicular  sides  :  let  a  solid,  S, 
whose  dimensions  are  to  be  ascertained,  be  now  plunged  in  the 
liquid.  The  space  which  the  solid  occupies  below  the  surface 
of  the  liquid  having  been  previously  filled  with  liquid,  the  liquid 
which  so  filled  it,  being  now  excluded,  must  find  room  else- 


00  A   TREATISE    ON   HYDROSTATICS.  CHAP.   V. 

where.  By  yielding  its  place  to  the  solid,  it  will  itself  displace 
the  adjacent  particles  of  liquid,  and  a  general  change  of  position 
will  take  place  in  the  whole  mass.  The  surface  E  F  will  rise 
to  the  level  E'  F'.  The  space  between  E  F  and  E'  F'  must  ev- 
idently be  equal  to  the  dimensions  of  the  solid  S,  because  it  is 
the  increased  space  which  the  liquid  occupies,  owing  to  the 
exclusion  of  part  of  it  from  the  space  now  occupied  by  the  solid. 
,  i  fact,  we  may  consider  that  portion  of  the  liquid  which  pre- 
viously occupied  the  space  S  to  be  removed  to  the  space  be- 
tween the  levels  E  F  and  E'  F'.  Thus,  by  means  at  once 
simple  and  easy,  we  have  obtained  a  body  E  F  F'  E',  of  a  regu- 
lar shape  and  easily  measured,  which  we  are  infallibly  certain 
is  equal  in  magnitude  to  the  irregular  solid  S,  the  dimensions 
of  which  we  would  in  vain  attempt  to  determine  by  the  nicest 
instrumental  measurement,  guided  by  the  strictest  mathemati- 
cal rules. 

If  we  conceive  the  vessel  A  B  C  D  to  be  of  glass*,  and  divis- 
ions marked  on  its  exterior  surface  by  parallel  lines  from  the 
bottom  to  the  top,  as  represented  in  the  figure,  the  interval  be- 
tween each  division  may  correspond  to  any  given  magnitude, 
as  a  cubic  inch  of  liquid.  The  whole  quantity  of  liquid  in  such 
a  vessel  will  be  expressed  by  the  number  which  marks  the  di- 
vision, and  the  fraction  of  a  division,  at  which  its  surface  stands. 
Thus  if  the  level  of  the  liquid  in  the  vessel  stand  at  one  third 
of  the  division  above  that  marked  5,  the  total  quantity  of  liquid 
in  the  vessel  will  be  5  J  cubic  inches.  Let  us  suppose  liquid  be 
poured  in  until  the  surface  rises  to  the  sixth  division :  let  it  be 
now  required  to  determine  the  magnitude  of  an  irregular  lump 
of  ore.  Plunge  it  in  the  liquid,  in  which  it  will  sink  by  its  su- 
perior weight,  and  observe  the  division  to  which  the  surface  has 
risen.  Suppose  this  to  be  one  fourth  of  a  division  above  the 
eighth.  It  appears,  then,  that  the  piece  of  ore  has  displaced  as 
much  liquid  as  would  raise  the  level  two  and  a  quarter  divis- 
ions ;  and,  therefore,  its  magnitude  is  two  and  a  quarter  cubic 
inches. 

We  have  here  supposed  that  we  possess  a  vessel  previously 
graduated,  so  that  each  division  shall  correspond  to  a  given 
quantity  of  liquid.  The  same  property  which  suggests  the  use 
of  such  a  vessel  also  suggests  the  method  of  graduating  it.  Let 
a  solid  be  formed  into  the  exact  shape  and  size  of  a  cubic  inch, 
and  some  liquid  having  been  poured  into  the  vessel  sufficient 
for  the  total  immersion  of  the  solid,  let  a  line  be  drawn  on  the 
vessel,  marking  the  place  of  its  surface ;  the  solid  being  then 
immersed,  let  another  line  be  drawn,  marking  the  place  to 
which  the  surface  of  the  liquid  has  risen.  The  interval  be- 
tween these  two  lines  will  then  be  a  division  which  corresponds 
to  a  cubic  inch  of  the  liquid.  If  the  sides  of  the  vessel  be  truly 


CHAP.  V.  MEASUREMENT    OF    SOLIDS.  61 

perpendicular,  and  its  inner  surface  subject  to  no  inequalities, 
nothing  more  will  now  be  necessary  than  to  draw  a  line  upon 
the  vessel  from  top  to  bottom,  and  to  divide  it  into  parts  equal 
to  the  space  we  have  just  obtained ;  each  division  will  then 
correspond  to  a  cubic  inch  of  the  liquid  :  the  divisions  may  evi- 
dently be  subdivided  into  fractional  parts  to  any  extent  that  may 
be  required. 

If,  however,  the  sides  of  the  vessel  be  not  perpendicular,  or 
being  so,  if,  as  will  inevitably  happen,  they  be  subject  to  ine- 
qualities more  or  less  in  amount  according  to  the  accuracy  with 
which  the  vessel  is  made,  then  the  method  of  division  which  we 
have  just  adopted  will  not  give  true  results.  It  is  only  where 
the  sides  of  the  vessel  are  uniform  from  top  to  bottom,  that 
equal  divisions  will  correspond  to  equal  quantities  of  the  liquid. 
If  one  part  be  wider  or  narrower  than  another,  an  equal  length 
of  that  part  will  contain  more  or  less  liquid  than  the  other  ;  and 
as  our  object  is  to  divide  into  equal  parts  the  liquid,  and  not  the 
height  of  the  vessel,  it  will  follow  that  the  degrees  must  be 
smaller  where  the  vessel  is  wider,  and  vice  versa.  Besides  the 
inequalities  incident  to  vessels  intended  to  be  straight,  it  does 
not  always  happen  that  such  a  vessel  is  convenient  for  use. 
The  graduated  vessels  used  by  apothecaries  and  others,  who 
have  occasion  for  exact  liquid  measures,  are  more  frequently 
of  the  tapering  form  of  a  wine-glass  ;  the  divisions  on  the  sides 
of  such  vessels  will  be  wider  near  the  bottom,  and  narrower 
near  the  top.  Such  a  vessel  may  be  graduated  by  repeatedly 
plunging  into  it  the  same  solid,  and  marking  the  changes  of 
level  which  it  produces,  filling  the  vessel  with  liquid  to  the  new 
division  each  time  the  solid  is  withdrawn  :  or  it  may  be  effect- 
ed by  continually  pouring  into  it  a  previously  ascertained  meas- 
ure of  liquid,  and  marking  the  successive  changes  of  level. 

The  effects  of  immersion  not  only  measure  the  total  dimen- 
sions of  a  solid,  but  also  determine  any  required  part  of  it.  If 
the  solid  be  only  partially  immersed,  that  part  which  is  below 
the  surface  of  the  liquid,  displacing  a  portion  of  the  liquid  equal 
to  its  own  bulk,  will  cause  the  surface  of  the  liquid  to  rise,  and 
the  space  through  which  it  rises  will  indicate  the  magnitude  of 
the  part  of  the  solid  which  is  immersed. 

A  solid  body  may  thus  be  easily  divided  into  two  or  more 
parts  having  any  given  proportion  to  each  other.  Suppose  it 
be  required  to  divide  a  solid  into  two  equal  parts.  Let  the  solid 
be  totally  immersed  in  a  liquid,  and  observe  the  height  to  which 
the  surface  of  the  liquid  rises.  Let  the  solid  be  now  withdrawn 
from  the  liquid,  and  let  it  again  be  partially  immersed  until  the 
surface  rise  through  half  the  former  space  ;  the  liquid  displaced 
will  then  be  half  the  quantity  which  was  displaced  by  the  total 
immersion  of  the  solid:  therefore  the  part  now  immersed  must 
6 


6  A    TREATISE    ON    HYDROSTATICS.  CHAP.    V. 

be  half  the  magnitude  of  the  whole.  If  a  line  be  marked  on 
the  solid  at  the  points  where  the  surface  of  the  water  meets  it 
a  division  made  through  this  line  will  divide  the  solid  into  two 
equal  parts.  In  the  same  manner,  if  it  were  required  to  cut  off 
a  fifth  part  of  the  entire  magnitude,  it  will  be  only  necessary 
to  immerse  it,  until  the  surface  of  the  water  rise  in  the  vessel 
through  a  space  equal  to  the  fifth  part  of  the  space  through 
which  it  would  be  raised  by  the  total  immersion.  It  is  evident 
that  a  similar  process  would  enable  us  to  cut  off  any  required 
part  of  the  body  ;  and  a  repetition  of  the  process  applied  to  the 
remainder  of  the  body  would  enable  us  to  cut  it  into  any  num- 
ber of  parts,  equal  or  unequal,  or  bearing  any  required  propor- 
tion to  each  other. 

There  are  circumstances  which  occasionally  impede  the 
practical  use  of  the  method  of  measuring  a  solid  by  immersion, 
ihus,  for  example,  if  the  solid  be  soluble  in  the  liquid,  the 
method  fails.  In  this  case,  however,  some  other  liquid  may 
generally  be  selected,  in  which  the  solid  is  not  soluble.  Again, 
the  body  be  of  such  an  open  or  porous  texture  as  to  allow  the 
liquid  to  penetrate  its  dimensions,  the  method  evidently  fails, 
because  the  solid  does  not  displace  a  quantity  of  the  liquid  equal 
to  its  magnitude.  The  liquid  which  enters  the  pores  still  occu- 
pies its  former  place  ;  and  the  portion  displaced  is,  in  fact,  only 
the  difference  between  a  quantity  of  liquid"  equal  in  bulk  to  the 
body,  and  the  quantity  which  the  body  absorbs.  If  the  absorp- 
tion of  the  liquid  do  not  affect  the  dimensions  of  the  solid,  the 
method  may  still  be  applied  by  saturating  the  solid  previously 
to  the  experiment  being  tried. 

From  what  has  been  stated  it  follows,  that  if  a  solid  be  pluno-- 
ed  into  a  vessel  filled  with  a  liquid,  as  much  of  the  liquid  wfll 
overflow  as  is  equal  to  the  magnitude  of  the  solid  immersed. 
And  a  vessel  which  is  only  partially  filled,  will  become  brimful 
by  the  immersion  of  a  solid,  whose  magnitude  is  equal  to  the 
part  unfilled.  Thus  a  teacup,  which  is  filled  to  the  brim  with 
tea,  will  overflow  when  sugar  is  put  in  ;  and  a  bath  should 
never  be  filled  beyond  such  a  height  as  will  allow  an  unfilled 
space  equal  to  the  aggregate  magnitude  of  the  bodies  of  the 
bathers. 

(52.}  We  have  seen  the  effect  which  the  immersion  of  a  solid 
produces  upon  the  volume  of  a  liquid.  This  effect  is  sometimes 
expressed  by  stating  that  the  volume  of  the  liquid  receives  an 
increase  equal  to  the  volume  of  the  solid ;  by  this,  however,  it 
is  not  meant  that  the  absolute  dimensions  or  measure  of  the 
liquid  are  increased,  but  merely  that  the  apparent  dimensions 
included  within  the  external  boundaries  of  the  liquid  are  aug- 
mented by  the  magnitude  of  the  solid.  In  fact,  the  contents  of 
the  vessel  in  this  case  are  the  liquid  and  the  solid  together ;  but 


CHAP.    V.  LOSS    OF    WEIGHT    BY    IMMERSION.  63 

the  solid  being  surrounded  with  the  liquid,  the  dimensions  of 
the  liquid  are  estimated  by  its  exterior  surfaces,  in  the  same 
manner  as  the  dimensions  of  a  rock  would  be  estimated  by  its 
external  limits,  even  though  it  should  contain  within  it  a  cavity 
filled  by  any  other  substance. 

We  shall  now  consider  what  effect  is  produced  upon  the  ap- 
parent weight  of  a  liquid  by  the  immersion  of  a  solid.  Let 
A  T$,Jig.  39.,  be  a  vessel  containing  a  liquid,  placed  in  the  dish 

Fig.  39. 


D  of  a  balance  E  F,  and  counterpoised  by  weights  in  the  oppo- 
site dish  G.  The  weights  in  G  will  then  be  equal  to  the  weight 
of  the  vessel  A  B,  and  the  weight  of  the  liquid  it  contains.  Let 
a  solid,  S,  heavy  enough  to  sink  in  the  liquid,  be  now  suspended 
by  a  horse  hair,  or  fine  thread,  from  an  arm  C,  and  let  the  arm 
C  be  so  placed  as  to  allow  the  solid  S  to  sink  into  the  liquid 
until  it  is  totally  immersed,  but  so  that  it  shall  not  touch  the 
bottom  of  the  vessel.  It  will  be  observed  that  the  dish  D  will 
immediately  preponderate,  the  weights  in  G  being  no  longer 
sufficient  to  counterpoise  the  weight  in  the  opposite  dish  D. 
Hence  we  infer  at  once,  that  as  the  apparent  dimensions  of  the 
liquid  were  increased  by  the  immersion  of  the  solid,  so  also  is 
the  apparent  weight  of  the  liquid  augmented.  But  the  amount 
of  this  increment  of  weight  is  still  to  be  found. 

Let  additional  weights  be  placed  in  the  dish  G  until  equilib- 
rium be  restored :  the  amount  of  these  weights  will  express 
the  increase  which  the  apparent  weight  of  the  liquid  receives 
from  the  immersion  of  the  solid.  Let  these  additional  weights 
be  now  removed,  and  let  the  solid  S  be  also  removed  from  the 
vessel  A  B.  The  balance  will  then  again  be  an  equilibrium. 
The  height  to  which  the  surface  of  the  liquid  in  the  vessel  A  B 
was  raised  by  the  immersion  of  the  solid  S  having  been  observ- 
ed, let  so  much  more  liquid  be  poured  into  the  vessel  A  B  as 
will  raise  the  surface  to  that  point.  This  quantity,  according 
to  what  has  already  been  explained,  is  equal  in. bulk  to  the 


64  A    TREATISE    ON    HYDROSTATICS.  CHAP.    V. 

solid  S  ;  and  by  the  weight  of  this  quantity  the  dish  D  will  now 
preponderate.  Let  the  weights  which  restored  the  equilibrium 
when  the  solid  was  formerly  immersed  be  now  again  placed  in 
the  dish  G,  and  equilibrium  will  be  once  more  restored.  It 
therefore  follows,  that  the  increase  which  the  apparent  weight 
of  the  liquid  receives  from  the  immersion  of  a  solid  is  equal  to 
the  weight  of  the  portion  of  liquid  which  the  solid  displaces. 

As  this  is  a  principle  of  the  highest  importance  in  the  theory 
of  fluids,  and  indeed  in  physical  science  generally,  it  may  not 
be  useless  here  to  present  its  experimental  illustration  under 
another  point  of  view.  Let  A  B  and  A'  B',  fg.  40.,  be  two 

Fig.  40. 


similar  and  equal  glass  vessels  of  equal  weight,  and  let  them 
be  filled  to  the  same  level  L  and  L',  with  water,  and  placed  in 
the  dishes  of  a  balance.  Being  of  equal  weight,  they  will  then 
be  in  equilibrium.  Let  a  solid  S,  suspended  as  in  the  former 
case,  be  immersed  in  A  B.  The  dish  D  will  preponderate  ;  and 
the  level  L  will  rise  to  I.  Let  water  be  now  poured  in  A7  B', 
until  the  equilibrium  be  restored.  It  will  be  found  that  the 
level  of  the  water  in  A'  B'  has  been  raised  through  the  same 
space  by  the  additional  water  necessary  to  restore  the  equilib- 
rium, as  the  level  of  the  water  in  A  B  has  been  raised  by  the 
immersion  of  the  solid.  The  conclusion  is  evident.  The  im- 
mersion of  the  solid  gives  to  the  vessel  an  increase  of  weight 
equal  to  that  which  it  would  receive  from  the  addition  of  so 
much  water  as  the  solid  displaces. 

(53.)  We  have  here  supposed  the  immersion  of  the  solid  to 
be  total ;  and,  consequently,  the  weight  imparted  to  the  liquid 
is  that  of  a  portion  of  the  liquid  itself  equal  to  the  whole  bulk  of 
the  solid.  But  the  same  experiments  will  give  similar  results, 
if  the  solid  be  only  partially  immersed.  Still  the  weight  which 
the  liquid  will  receive,  will  be  equal  to  the  weight  of  that  por- 
tion of  it  which  will  be  displaced  by  the  part  of  the  solid  immers- 
ed. It  will  not  be  necessary  here  to  repeat  the  experimental 


CHAP.    V.  EFFECTS    OF    IMMERSION.  65 

process  by  which  this  is  verified ;  it  is  the  same,  in  all  respects, 
as  has  been  already  explained  with  reference  to  total  immersion. 

The  manner  in  which  the  immersion  of  the  solid  has  been 
described  in  the  preceding  experiments,  by  suspending  it  from 
the  arm  C  by  a  thread  or  hair,  requires  that  the  solid  should  be 
one  which,  by  its  weight  alone,  will  sink  in  the  liquid.  The 
conclusions  at  which  we  have  arrived  are  not,  however,  limited 
to  such  bodies.  If,  therefore,  the  solid  to  be  immersed  be  one 
so  light  that  it  would  float  on  the  liquid,  its  immersion  must  be 
produced  by  a  different  means ;  it  must  be  pressed  into  the 
liquid  by  a  rigid  inflexible  wire,  or  some  other  means.  When 
this  is  accomplished,  however,  all  the  results  are  conformable 
to  what  has  been  already  explained. 

From  all  which  has  been  stated,  we  may,  therefore,  infer  that 
the  immersion  of  any  solid,  whether  total  or  partial,  increases 
both  the  apparent  bulk  and  the  apparent  weight  of  the  liquid ; 
and  that  it  increases  both  exactly  in  that  degree  in  which  they 
would  be  increased  by  the  addition  of  so  much  of  the  same  liquid 
as  is  equal  in  magnitude  to  the  immersed  solid. 

(54.)  The  weight  both  of  the  liquid  and  the  solid  immersed 
in  it,  depends  on  the  attraction  which  the  earth  exerts  on  their 
particles  ;  and,  therefore,  so  long  as  the  mass  of  the  liquid  and 
the  mass  of  the  solid  remain  unaltered,  their  weights  in  the 
same  place  must  be  immutable.  It  follows,  therefore,  that  the 
increase  of  weight  which  the  vessel  receives  from  the  immer- 
sion of  the  solid  cannot  proceed  from  any  increase  of  weight  in 
either  the  vessel  or  the  liquid,  nor  can  it  proceed  from  any  in- 
crease or  diminution  in  the  weight  of  the  solid  immersed  ;  the 
mere  fact  of  immersion  can  cause  no  change  in  the  amount  of 
these  weights. 

It  is  natural,  therefore,  to  inquire  whence  the  increase  of 
weight  which  the  vessel  receives  by  the  immersion  of  the  solid 
proceeds.  We  have  seen  that  the  actual  weight  of  the  water 
contained  in  the  vessel  remains  unaltered,  while  its  apparent 
weight  is  increased.  We  know  that  the  actual  weight  of  the 
solid  cannot  be  altered ;  but  it  is  still  to  be  seen  how  its  ap- 
parent weight  is  affected.  Let  us  suppose  the  solid  immersed 
to  be  heavier  than  water,  and  let  it  be  suspended  from  the  arm 
of  a  balance,  as  represented  in  jig.  41.,  and  counterpoised.  Let 
it  then  be  immersed  in  the  liquid  contained  in  the  vessel,  as  icp- 
resented  in  the  figure.  Immediately  the  equilibrium  will  be 
destroyed ;  the  dish  G  will  preponderate,  and  the  arm  E  will 
rise  :  it  therefore  appears  that  by  immersion  the  apparent  weight 
of  the  solid  is  diminished.  Let  us  now  inquire  the  amount  of 
this  diminution.  Remove  from  the  dish  G  such  a  quantity  of 
weight  as  will  restore  the  equilibrium,  so  that  the  dish  G  will 
no  longer  preponderate,  but  will  exactly  counterpoise  the  weight 
6* 


66  A    TREATISE    ON    HYDROSTATICS.  CHAP.    V. 

suspended  from  E.  The  weight  thus  removed  is  the  amount 
by  which  the  apparent  weight  of  the  solid  is  diminished  by  im- 
Let  the  quantity  of  the  liquid  be  obtained  by  means 

Fig.  41. 
3D 


of  a  balance,  the  weight  of  which  is  equal  to  the  weight  remov- 
ed from  the  dish  G.  Let  the  level  at  which  the  liquid  stands 
in  the  vessel  A  B  be  marked  on  its  side,  and  let  the  solid  be 
then  removed  from  it ;  the  surface  of  the  liquid  will  immediate- 
ly fall,  leaving  a  space  between  its  former'  and  present  level 
equal  to  the  magnitude  of  the  solid.  Let  the  liquid,  whose 
weight  was  ascertained  to  be  that  which  was  lost  by  the  appar- 
ent weight  of  the  solid,  be  snow  poured  into  the  vessel  A  B,  the 
surface  will  rise  to  the  point  at  which  it  stood  when  the  solid 
was  immersed. 

Hence  it  must  be  evident, 

1.  That  by  the  process  of  immersion,  while  the  apparent 
weight  of  the  liquid  is  increased,  the  apparent  weight  of  the 
solid  is  diminished ; 

2.  That  the  increase  which  the  apparent  weight  of  the  liquid 
receives  is  exactly  equal  to  the  diminution  of  the  apparent 
weight  of  the  solid  ;  and, 

3.  That  the  amount  of  this  increment  of  the  one  apparent 
weight,  and  decrement  of  the  other,  is  the  weight  of  a  portion 
of  the  liquid  whose  magnitude  is  equal  to  the  magnitude  of  the 
solid. 

If  we  pursue  these  conclusions  into  their  consequences,  we 
shall  obtain  some  remarkable  results.  Suppose  it  should  so 
happen,  that  the  body  selected  for  immersion  is  one  whose 
weight  is  equal  to  the  weight  of  its  own  bulk  of  the  liquid  ;  by 
the  principles  just  established  it  will  lose  by  immersion  its  whole 
weight ;  and,  consequently,  when  immersed,  if  it  were  suspend- 
ed from  the  arm  of  a  balance,  it  would  weigh  nothing  ;  that  is, 
the  thread  which  connects  it  with  the  arm  would  be  stretched 
by  no  force,  and  the  body  would  have  no  tendency  to  descend : 


CHAP.    V.  EFFECTS    OF    IMMERSION.  67 

and,  accordingly,  we  find  this  to  be  actually  the  case.  Let  a 
hollow  brass  ball  be  provided,  with  a  means  of  enclosing  fine 
sand  within  it ;  by  this  means  let  the  weight  of  the  ball  be  so  ad- 
justed as  to  be  equal  to  that  of  its  own  bulk  of  water,  and  let  it  be 
thrown  into  a  vessel  of  that  liquid.  It  will  be  found  that  it  will 
remain  suspended  indifferently  in  any  position,  provided  it  be 
totally  immersed.  If  it  be  placed  at  the  bottom,  there  it  will 
remain  ;  if  it  be  placed  any  where  between  the  surface  and  the 
bottom,  it  will  also  remain  suspended  there  ;  if  it  be  placed  at 
the  surface,  but  so  that  no  part  shall  be  above  it,  there  it  will 
also  remain. 

There  is  another  remarkable  consequence  obviously  collected 
from  what  has  been  proved.  If  the  solid  immersed  in  a  liquid 
have  less  weight  than  its  own  bulk  of  the  liquid^  it  would  fol- 
low, by  total  immersion,  it  loses  more  than  its  own  weight ;  a 
consequence  not  as  absurd  as  it  may  at  first  seem  to  be.  When 
a  body,  by  immersion,  loses  less  than  its  whole  weight,  it  has  a 
tendency  to  descend  with  what  remains.  When  a  body  loses 
exactly  its  whole  weight,  the  effect  of  its  gravity  is  neutralized, 
and  it  loses  all  tendency  to  move,  as  in  the  example  just, pro- 
duced. But  when  the  consequences  would  justify  us  in  affirm- 
ing that  it  loses  more  than  its  entire  weight,  the  effect  is  man- 
ifested not  merely  by  the  body  losing  all  tendency  to  sink,  not 
merely  by  lying  passively  in  the  liquid,  but  by  exhibiting  a  posi-  ; 
tive  tendency  to  rise  ;  by  acquiring,  in  fact,  a  quality  the  very  ; 
reverse  of  weight.  Those  who  have  been  used  to  the"  significa-  ] 
tion  of  negative  signs  in  algebra  will  perceive  the  tendency  of  \ 
this  reasoning,  and  will  find  in  it  the  illustration  of  the  true 
meaning  of  such  symbols.  For  those  who  are  not  conversant 
with  the  elements  of  mathematics,  it  is  hoped  that  enough  has 
been  said  to  elucidate  the  utility  of  extending  the  application 
of  a  theorem,  by  giving  a  greater  latitude  to  the  signification  of 
the  terms  in  which  it  is  expressed. 

The  phenomena  of  floating  bodies  are  verifications  of  the  in- 
ference which  has  just  been  made.  Let  the  hollow  brass  ball,  ' 
already  alluded  to,  be  so  loaded  that  it  shall  be  lighter  by  any 
proposed  weight  than  its  own  bulk  of  water  ;  let  it  then  be  im- 
mersed in  a  vessel  of  that  liquid,  and  placed  below  the  surface. 
It  will  be  found  that  the  ball  will  not  remain  there,  but  will 
ascend  to  the  surface,  on  which  it  will  float.  To  keep  it  below 
the  water,  a  certain  force  will  be  necessary ;  and  if  this  force 
be  measured,  it  will  be  found  to  be  equal  to  the  excess  of  the 
weight  of  a  portion  of  liquid  equal  in  bulk  to  the  ball  above  the 
weight  of  the  ball. 

The  conclusions  to  which  we  have  arrived  may,  therefore,  be 
generalized  as  follows  : — 

1.  A  solid  whose  weight  exceeds  the  weight  of  its  own  bulk 


68 


A    TREATISE    ON    HYDROSTATICS. 


CHAP. 


of  a  liquid  has  a  tendency  equal  to  such  excess  to  sink  when  im- 
mersed in  the  liquid. 

2.  A  solid  whose  weight  is  equal  to  the  weight  of  its  own 
bulk  of  liquid,  when  immersed  in  the  liquid,  has  no  tendency  to 
sink  or  rise. 

3.  A  solid  whose  weight  is  less  than  the  weight  of  its  own 
bulk  of  a  liquid  has  a  tendency  to  rise  when  immersed  in  that 
liquid  ;  which  tendency  amounts  to  the  excess  of  the  weight  of 
a  portion  of  the  liquid  equal  in  bulk  to  the  solid  above  the  weight 
of  the  solid. 

(55.)  The  reasoning  by  which  we  have  arrived  at  these  con- 
clusions has  been  founded  on  the  results  of  the  experiments 
Described  in  (52.).  They  may,  however,  be  inferred  from  the 
Aindamental  principle  of  HYDROSTATICS  ;  viz.  that  fluids  trans- 
.nit  pressure  equally  in  all  directions. 

Let  us  suppose  a  solid,  A  B  C  D,  Jig,  42.,  of  any  proposed 

Fig.  42. 


figure,  as  that  of  a  cubic  inch,  immersed  in  a  liquid,  the  surface 
of  which  is  L  M,  and  let  I/  M'  be  the  level  on  which  the  bot- 
tom B  C  is  placed.  Let  the  solid  be  suspended  by  a  fine  thread 
T,  the  weight  of  which  may  be  neglected  ;  and  let  this  thread 
be  carried  over  a  grooved  wheel  R,  such  a  weight  W  being  ap- 
pended to  it  as  will  counterpoise  the  solid  A  B  C  D,  and  keep 
it  suspended  in  the  liquid  without  either  rising  or  sinking.  In 
this  state  every  part  of  the  level  L'  M'  must  sustain  the  same 
pressure  downward ;  for,  if  any  one  part  suffered  a  greater 
pressure  than  another,  the  liquid  below  the  level  L'  M'  would 
transmit  the  greater  pressure  undiminished  in  the  upward  direc- 
tion to  the  point  where  the  lesser  pressure  is  supposed  to  act ; 
and  this  point  would  move  upwards,  by  reason  of  the  excess  of 
the  upward  pressure ;  but  no  such  effect  is  supposed  to  take 
place,  and  therefore  no  part  of  the  level  L'  M'  is  under  a  greater 
pressure  than  another. 


CHAP.    V.  EFFECTS    OF    IMMERSION.  W* 

The  bottom  B  C  of  the  solid  occupies  a  square  inch  of  the 
level  L/  M'.  Let  the  column  resting  on  B  C,  of  which  the  solid 
forms  a  part,  be  imagined  to  be  continued  to  the  surface.  It  is 
evident  that  the  downward  pressure  excited  on  the  base  B  C 
will  be  equal  to  the  weight  of  the  incumbent  column  E  B  C  F 
diminished  by  the  weight  of  the  counterpoise  W.  This  column 
consists  partly  of  the  liquid  E  A  D  F,  which  is  above  the  solid, 
and  partly  of  the  solid  itself.  Since  this  downward  pressure  is 
sustained  by  the  stratum  L'  M7  at  B  C,  it  folloAvs  that  every 
part  of  that  stratum  equal  in  magnitude  to  B  C  must  sustain 
the  same  downward  pressure.  Take  H  B,  equal  to  B  C,  and 
the  part  H  B  sustains  a  pressure  arising  from  the  weight  of  the 
column  of  liquid  G  H  B  E,  which  rests  upon  it.  The  weight  of 
this  column  must,  therefore,  be  equal  to  the  weight  which  presses 
on  B  C. 

Let  us  suppose  the  column  G  H  B  E  divided  into  two  at  I  A ; 
so  that  the  part  I  A  B  H  shall  be  equal  in  bulk  to  the  solid 
A  B  C  D,  and  the  part  I  A  E  G  equal  to  the  liquid  E  A  D  F 
above  the  solid.  Let  us  now  compare  the  equal  pressures 
which  act  on  B  C  and  B  H.  The  former  is  the  weight  of 
E  A  D  F,  together  witl^  the  weight  of  the  solid  diminished  by 
the  weight  of  the  counterpoise  W.  The  latter  is  the  weight 
of  G  I  A  E,  together  with  the  weight  of  I  A  B  H.  It  appears, 
therefore,  that  the  weight  of  the  column  E  B  C  F  exceeds  that 
of  the  column  G  H  B  E  by  the  weight  W.  But  since  the  part 
E  A  D  F  of  the  first  column  is  equal  in  weight  to  the  part 
G  I  A  E  of  the  second,  it  follows  that  the  weight  of  the  solid 
A  B  C  D  exceeds  the  weight  of  its  own  bulk  I  A  B  H  of  the 
liquid  by  the  weight  of  the  counterpoise  W. 
/  Now,  since  the  counterpoise  W  is  the  force  which  prevents 
the  solid  from  sinking,  it  expresses  the  tendency  of  the  solid  to 
sink,  and  it  therefore  follows,  that  this  tendency  is  estimated  by 
the  excess  of  the  weight  of  the  solid  above  the  weight  of  its 
own  bulk  of  the  liquid,  according  to  what  has  already  been  ex- 
perimentally established. 

In  the  preceding  reasoning,  the  solid  has  been  supposed  to 
exhibit  a  tendency  to  sink  when  immersed  in  the  fluid,  which  ten- 
dency has  been  checked  by  the  counterpoise.  Let  us  now 
consider  the  case  of  a  solid  which  remains  suspended  in  the 
liquid  without  any  tendency  to  sink  or  rise.  In  this  case  the 
pressure  on  B  C,  jig.  43.,  is  the  weight  of  the  solid,  together 
with  that  of  the  fluid  above  it ;  while  the  pressure  on  H  B  is 
equal  to  the  weight  of  the  liquid  I  A  B  H,  equal  in  bulk  to  the 
solid,  together  with  the  weight  of  the  liquid  G  I  A  E  equal  to 
the  liquid  above  the  solid  ;  since  the  pressure  on  H  B  and  B  C 
must  be  equal,  the  weights  of  the  columns  G  H  B  E  and  E  B  C  F 
are  equal.  From  these  equals  take  away  the  weights  of  the 


70 


A    TREATISE    ON    HYDROSTATICS. 


CHAP.    V. 


liquid  G  I  A  E  and  E  A  D  F  respectively,  and  the  remainder*, 
which  are  the  weights  of  the  solid  and  its  own  bulk  of  liquid, 
will  be  equal.  Thus,  in  conformity  with  the  results  of  experi- 

Fig.  43. 


ment,  it  appears  that  a  solid  which  remains  suspended  in  a 
liquid  must  be  equal  to  the  weight  of  the  liquid  which  it  dis-" 
places. 

Finally,  let  us  consider  the  case  in  which  the  solid  immersed 
has  a  tendency  to  rise  to  the  surface  ;  suppose  a  fine  thread 
attached  to  the  bottom  of  the  solid  to  be  carried  under  a  groov- 
ed wheel  R/,/g*.  44.,  and,  being  brought  upwards,  to  be  passed 

Fig.  44. 


over  another  grooved  wheel  R,  and  let  such  a  weight,  W,  be 
appended  to  it  as  will  check  the  tendency  of  the  solid  to  rise  to 
the  surface,  but  not  sufficient  to  cause  it  to  sink.  The  solid 
A  B  C  D  therefore  remains  suspended  in  the  liquid. 

According  to  the  reasoning  used  in  the  former  cases,  it  may 
be  inferred  that  the  pressure  on  B  C  must  be  equal  to  the  pres- 
sure on  B  H.  The  pressure  on  B  C  is  equal  to  the  weight  of 
the  solid,  the  liquid  above  it,  and  the  counterpoise  W.  The 


CHAP.    V.  EFFECTS    OF    IMMERSION.  71 

pressure  on  B  H  is  equal  to  the  weight  of  the  liquid  I  A  B  H, 
equal  in  bulk  to  the  solid,  together  with  the  weight  of  G  E  A  I, 
equal  to  the  weight  of  the  liquid  above  the  solid!  From  these 
equals  take  away  G  E  A  I  and  E  F  D  A,  and  the  remainders 
will  be  equal ;  that  is,  the  liquid,  equal  in  bulk  to  the  solid,  will 
be  equal  to  the  weight  of  the  solid,  together  with  the  counter- 
poise W.  It  therefore  appears,  that  a  portion  of  the  liquid 
equal  in  bulk  to  the  solid  exceeds  the  weight  of  the  solid,  by 
that  weight  which  is  just  sufficient  to  prevent  the  solid  ascend- 
ing to  the  surface  and  to  keep  it  suspended  in  the  liquid.  Hence, 
in  conformity  with  what  has  already  been  experimentally  prov 
ed,  it  appears  that  a  solid  lighter  than  its  own  bulk  of  the  liquid 
has  a  tendency,  when  immersed  in  the  liquid,  to  rise  to  the 
surface  with  a  force  equal  to  the  difference  between  its  weight 
and  that  of  its  own  bulk  of  the  liquid. 

The  fact  that  a  solid  equal  in  weight  to  its  own  bulk  of  liquid 
will  remain  suspended  indifferently  in  any  position  in  the  liquid, 
may  also  be  very  easily  comprehended,  by  considering  that  the 
liquid  itself  remains  quiescent.  If,  then,  we  take  any  portion 
of  the  liquid  beneath  its  surface,  say  a  cubic  inch  at  the  depth 
of  one  foot,  that  cubic  inch  of  liquid  remains  at  rest.  Suppose 
it  now  to  be  congealed  and  to  become  solid, — not,  however, 
altering  in  any  way  its  bulk, — it  will  evidently  still  remain  at 
rest,  because  the  fact  of  it  becoming  solid  introduces  no  force 
to  put  it  into  motion.  It  will,  therefore,  be  in  the  case  of  any 
solid  immersed  in  the  liquid  equal  in  weight  to  the  liquid  which 
it  displaces. 

But  it  will  be  more  philosophical  to  deduce  the  fact  of  the 
suspension  of  the  solid  from  the  reasoning  already  given,  and 
founded  on  the  distinctive  property  by  which  a  fluid  transmits 
pressure  ;  and  this  same  property  is  that  on  which  the  quiescence 
of  all  parts  of  a  liquid  depends. 

(56.)  We  have  hitherto  considered  the  cases  only  in  which  the 
solid  is  totally  immersed.  The  effects  of  partial  immersion  are 
in  all  respects  similar,  and  investigated  on  the  same  principles. 

Let  A  B  C  D,  fig.  45.,  be  a  solid  partially  immersed  in  a 
liquid  whose  surface  is  L  M,  and  having  a  tendency  to  sink 
still  deeper,  which  tendency  is  checked  by  the  counterpoise  W. 
Since  the  solid  is  in  equilibrium,  the  stratum  L'  W  of  the  liquid, 
immediately  below  its  base,  must  be  equally  pressed  in  every 
part.  The  pressure  on  B  C  is  equal  to  the  weight  of  the  solid 
diminished  by  the  counterpoise  W.  Let  H  B  be  a  portion  of 
the  stratum  equal  to  B  C ;  the  pressure  here,  which  is  equal  to 
the  former,  is  the  weight  of  the  column  G  H  B  E.  This  column 
is  evidently  equal  to  the  weight  of  the  liquid  displaced  by  the 
solid  ;  and  therefore  it  follows,  that  the  weight  of  the  liquid 
displaced  by  the  solid  is  equal  to  the  weight  of  the  solid  dimin- 


72  A   TREATISE    ON    HYDROSTATICS.  CHAP.  V. 

ished  by  that  of  the  counterpoise  ;  or,  what  amounts  to  the 
same,  the  weight  of  the  counterpoise  is  equal  to  the  excess  of 
the  solid  above  that  of  the  liquid  which  it  displaces.  Thus  the 


.same  property  belongs  to  the  partial  immersion  of  the  solid,  as 
has  been  already  proved  to  appertain  to  total  immersion. 

This  result  may  be  verified  experimentally,  by  attaching  the 
thread  which  supports  the  solid  A  B  C  D  to  the  arm  of  a  bal- 
ance, and  ascertaining  the  weight  from  the  opposite  arm  which 
will  support  it.  This  being  done,  and  the  level  of  the  surface 
L  M  being  observed,  let  the  solid  be  removed  from  the  liquid  ; 
the  counterpoise  from  the  opposite  arm  will  no  longer  be  able 
to  sustain  the  solid.  Let  such  an  additional  weight  be  added 
as  will  support  it,  and  take  a  quantity  of  the  liquid,  the  weight 
of  which  is  equal  to  this  additional  weight.  This  quantity, 
being  poured  into  the  vessel,  will  restore  the  level  L  M  to  its 
former  height :  hence  it  appears  that  this  quantity  is  equal  in 
magnitude  to  the  part  of  the  solid  which  was  immersed. 

If  the  solid  partially  immersed  have  no  tendency  either  to 
sink  or  rise,  the  counterpoise  W  will  be  unnecessary.  In  this 
case  the  pressure  on  B  C,Jig.  46.,  is  equal  to  the  weight  of  the 
solid  ;  and  the  equal  pressure  on  H  B  is  equal  to  the  weight  of 
the  liquid  displaced  by  the  solid.  Hence  it  follows,  that  when 
a  solid  floats  on  a  liquid,  it  displaces  as  much  liquid  as  is  equal 
to  its  own  weight. 

This  may  be  verified  experimentally.  Let  a  solid  which 
floats  on  a  liquid  be  first  weighed,  and  let  a  portion  of  the 
liquid  of  equal  weight  be  ascertained.  Let  the  level  of  the 
liquid  in  a  vessel  be  observed,  and  let  the  change  of  this  level 
be  ascertained,  which  is  produced  by  the  solid  floating  on  its 
surface.  It  will  be  found  that  the  same  change  of  level  will 
be  produced  by  pouring  into  the  vessel  as  much  liquid  as  is 


CHAP.    V. 


FLOATING*    BODILfc. 


73 


equal  to  the  weight  of  the  solid.  If  it  be  remembered  that  the 
change  of  level  is  owing  to  the  space  beneath  the  surface  of 
the  liquid  occupied  by  the  solid,  it  will  be  easily  understood 


that  the  portion  of  liquid  displaced  by  the  solid  is  that  which  is 
necessary  to  produce  the  same  change  of  level,  and  this  portion 
is  equal  in  weight  to  the  solid. 

It  may  happen  that  a  solid  partially  immersed  has  a  tendency 
to  rise.  Let  this  tendency  be  checked  by  the  force  of  the 
weight  W,  Jig.  47.,  drawing  the  solid  downwards.  The  pres- 


sure on  B  C  is  here  equal  to  the  weight  of  the  solid,  together 
with  the  weight  W  ;  and  this,  as  before,  is  equal  to  the  weight 
of  G  E  B  H,  the  liquid  displaced  by  the  solid.  Hence  it  appears 
that  W,  which  expresses  the  tendency  of  the  solid  to  rise,  is 
equal  to  the  excess  of  the  weight  of  the  fluid  displaced  by  the 
solid  above  the  weight  of  the  solid. 


74  A    TREA.*»3E    ON    HYDROSTATICS.  CHAP.    V. 

This,  also,  may  be  verified  experimentally,  by  removing  the 
weight  W,  and  connecting  the  string  with  the  arm  of  a  balance. 
It  will  be  found  that  the  counterpoising  weight,  together  with 
the  weight  of  the  solid,  is  equal  to  the  weight  of  as  much  liquid 
as  would  produce  the  same  change  of  level  as  is  produced  by 
the  partial  immersion  of  the  solid. 

The  consequences  which  have  been  just  inferred  are  so  im- 
portant, that  it  may  be  useful  here  to  recapitulate  them. 

Whenever  a  solid  is  immersed  in  a  liquid,  whether  the  im- 
mersion be  partial  or  total,  it  will  have  a  tendency  to  sink,  if 
its  weight  be  greater  than  the  weight  of  the  liquid  which  it  dis- 
places. 

It  will  have  a  tendency  to  rise  if  the  weight  be  less  than  that 
of  the  liquid  which  it  displaces. 

It  will  have  no  tendency  either  to  rise  or  sink  if  its  weight 
be  equal  to  that  of  the  liquid  which  it  displaces. 

No  solid  can  float  on  the  surface  of  a  liquid  if  it  be  heavier 
than  its  own  bulk  of  the  liquid  ;  because,  in  order  to  float  it  is 
necessary  that  the  liquid  displaced  be  equal  in  weight  to  the 
solid,  which  it  cannot  be,  if  the  weight  of  the  solid  be  greater 
than  that  of  its  own  bulk  of  the  liquid. 

In  whatever  position  a  body  floats,  it  will  always  displace  the 
same  quantity  of  liquid,  because  it  will  always  displace  a  por- 
tion of  liquid  equal  to  its  own  weight. 

The  effect,  therefore,  of  immersion  in  every  case  is  to  lessen 
the  apparent  weight  of  the  solid  immersed  by  affording  support 
to  its  real  weight. 

(57.)  The  support,  whether  partial  or  total,  which  a  solid  thus 
receives  from  a  liquid,  is  an  effect  with  which  every  one  is  fa- 
miliar, and  which  is  commonly  expressed  by  the  term  buoyancy. 
From  the  results  which  have  been  just  established,  it  appears 
that  a  solid  is  buoyant  in  a  liquid,  in  proportion  as  it  is  light  and 
as  the  liquid  is  heavy.  Thus  the  same  solid  will  be  more  buoy- 
ant in  quicksilver  than  in  water  ;  and  in  the  same  liquid  cork  is 
more  buoyant  than  lead.  Again,  a  solid  which  has  buoyancy 
enough  to  float  in  one  liquid  will  sink  in  another.  Thus  glass 
will  sink  in  water  but  will  float  in  quicksilver.  A  block  of  lig- 
numvitse,  or  a  piece  of  ebony,  will  sink  in  alcohol  but  will  float 
in  mercury.  A  block  of  ash  or  beech  will  float  in  water  but 
will  sink  in  sulphuric  ether.  The  reason  is,  that  the  weight  of 
glass  is  greater,  bulk  for  bulk,  than  that  of  water,  and  is  less 
than  that  of  mercury.  The  weight  of  lignum vitae,  or  ebony,  is 
greater,  bulk  for  bulk,  than  that  of  alcohol,  but  less  than  that 
of  water ;  and  the  weight  of  ash  or  beech  is  less,  bulk  for 
bulk,  than  that  of  water,  but  greater  than  that  of  sulphuric 
ether. 
Tf  a  rope  be  attached  to  a  heavy  block  of  stone  at  the  bottom 


CHAP.  V.  BUOYANCY.  75 

of  a  reservoir  of  water,  it  may  be  raised  to  the  surface  by  the 
strength  of  a  man  ;  but  as  soon  as  any  quantity  of  it  emerges 
from  the  surface,  the  same  strength  will  be  insufficient  to  sup- 
port it ;  it  loses  the  support  of  the  water,  and  requires  for  its 
support  as  much  more  force  as  is  equal  to  the  weight  of  the 
water  which  it  has  displaced.*  In  building  piers  and  other  sub- 
aqueous works,  this  effect  is  rendered  peculiarly  manifest ;  the 
laborer  feels  himself  endued  with  prodigiously  increased 
strength,  raising  with  ease,  and  adjusting  in  their  places,  blocks 
of  stone,  which  he  would  in  vain  attempt  to  move  above  the 
water.  Such  operations  are  carried  on  by  the  aid  of  a  diving 
bell,  a  contrivance  which  will  be  explained  in  a  succeeding  part 
of  this  volume.  After  a  man  has  worked  for  any  considerable 
time  in  this  way  under  water,  he  finds,  upon  removing  to  the 
air,  that  he  is  apparently  weak  and  feeble  :  every  thing  which 
he  attempts  to  lift  seems  to  have  unusual  weight ;  and  to  move 
even  his  own  limbs  is  attended  with  some  inconvenience. 

(58.)  Every  one  who,  while  bathing,  has  walked  in  the  water, 
is  sensible  how  small  a  weight  rests  upon  the  feet.  If  the  depth 
be  so  great  that  the  body  is  immersed  to  the  shoulders,  the  feet 
are  scarcely  sensible  of  any  pressure  on  the  bottom.  The  want 
of  sufficient  pressure  in  this  case  renders  the  body  easily  upset. 
In  attempting  to  ford  a  river  in  which  there  is  a  current,  con- 
siderable danger  is  produced  by  this  cause ;  even  though  the 
river  should  be  sufficiently  shallow  to  leave  a  large  portion  of 
the  body  above  the  surface.  The  pressure  on  the  bottom  being 
diminished  by  the  buoyancy  of  the  liquid,  the  feet  have  a  less 
secure  hold  on  the  ground,  and  the  force  of  the  current,  acting 
on  that  part  of  the  body  which  is  immersed,  without  affecting 
*hat  part  which  is  above  the  surface,  has  a  tendency  to  carry 
-way  the  support  of  the  feet. 

A  body  composed  of  any  material,  however  heavy,  may  be  so 
formed  as  to  float  upon  any  liquid,  however  light.  To  effect 
this  it  is  only  necessary  to  give  it  such  a  shape  as  will  cause  it 
to  displace  a  quantity  of  liquid,  which  is  as  many  times  greater 
than  its  absolute  bulk,  as  its  weight  is  greater  than  that  of  an 
equal  bulk  of  the  liquid.  There  are  an  infinite  variety  of  figures 
which  will  accomplish  this.  A  basin  formed  of  porcelain,  brass, 
or  any  heavier  material,  will  float  upon  water  if  it  be  placed 
with  its  convex  side  towards  the  liquid.  The  water  being  ex- 
cluded from  the  interior  of  the  basin,  as  much  liquid  will  be 
displaced  as  would  be  equal  to  the  bulk  of  that  part  of  the  basin 
which  is  immersed,  if,  instead  of  being  hollow,  it  were  filled  to 
the  level  of  the  liquid  in  the  vessel.  But  if  the  basin  be  im- 
mersed with  its  concave  side  downwards,  the  water  entering 

*  That  is,  "  the  water  which  had  been  previously  displaced  by  the  part  wbioh 
has  now  emerged." — AM.  ED.. 


A    TREATISE    O*    1IY0KOSTATIC8.  CHAP.    V. 

flbe  hollow  of  the  vessel,  H  can  displace  no  more  water  than  w 
equal  to  the  actual  bulk  of  material  which  compose*  the  basin  ; 
and  this  material  being  heavier,  bulk  for  bulk,  than  water,  it  wffl 


(59.  \,od  of  adapting  the  shape  of  a  body  heavier, 

balk  for  balk,  than  a  liquid,  so  as  to  cause  it  to  float,  depends 
on  giving  it  such  a  shape  as  that,  when  immersed  in  the  water, 
there  will  be,  below  the  level  of  the  liquid,  some  space  in 
the  vessel  occupied  by  air  or  by  some  substance  lighter  than 
the  liquid.  Thus  if  a  teacup  be  placed  with  its  bottom  down- 
ward* on  the  surface  of  water  contained  in  a  basin,  it  will  float  ; 
bat  if  the  depth  to  which  it  sinks  be  observed,  it  will  be  found 
that  a  part  of  the  hollow  of  the  cop  is  below  the  surface  of  the 
water.  In  this  case,  therefore,  the  space  below  the  level  of  the 
liquid  k  occuoied  partly  by  the  porcelain  of  which  the  cap  is 
compose^  and  j^y  by  the  portion  of  air  which  occupies  that 
part  of  the  hollow  of  the  cap  below  the  surface  of  the  water. 
It  is  the  lightness  of  this  portion  of  air,  compared  with  water, 
which  enable*  the  cup  to  float  That  this  is  the  case  may  be 
proved  by  the  following  experiment  Let  water  be  poured  into 
the  cop  thus  floating,  and  observe  the  level  of  the  water  in  the 
cop  and  in  the  vessel  ;  the  former  will  always  be  found  below 
the  latter;  00  that  a  stratum  of  air  still  lies  below  the  level  of 
water  in  the  basin.  And  this  will  be  the  case  until  the  cup  be 
completely  filled  with  water,  when,  no  space  being  left  for  air 
below  the  surface,  the  cup  will  sink  to  the  bottom, 

For  these  reasons  a  ship  or  boat,  composed  of  a  material 

which  is  heavier,  bulk  for  bulk,  than  water,  will  sink  when  filled 

with  water  by  aleak  or  otherwise  ;  bat  if  the  material  be  lighter, 

•he  will  continue  to  float,  though  at  an  increased  depth  :  in  such 

a  case  the  ship  i*  said  to  be  water-logged.    Many  ships  are 

made  of  a  sort  of  Umber,  snch  as  teak,  which  is  heavier,  bulk 

k,  than  water,    And,  indeed,  if  the  average  weight  of  all 

*terials  w  into  the  construction  of  an  ordinary 

vessel  be  taken,  it  is  probable  that  they  are  heavier  thar 

>ulk  of  water.  Whether  a  vessel,  however,  wffl  sink  by 
being  water-lodged,  will  depend  as  much  upon  the  nature  of 
the  cargo  a*  the  vessel  itself,  A  vessel  laden  with  iron,  or 
with  any  other  heavv  substance,  will,  in  such  a  case,  sink  ;  while 
one  laden  with  cork,  timber,  or  any  other  light  substance,  will 

(60.)  An  iron  boat  will  float  with  perfect  security  ;  and,  if  H 
be  formed  with  double  plates  of  metal,  including  between  them 
a  sufficient  hollow  space,  and  so  united  as  to  exclude  the  water, 
no  circumstance  can  sink  it;  for,  whatever  be'  its  position,  it 
"iD  displace  more  water  than  is  equal  to  Hs  own  weight 

A  contrivance  to  prevent  ships  foundering  at  sea,  founded  on 


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78  A   TREATISE    ON    HYDROSTATICS.         (    CHAP.    V. 

the  extremity  of  this  pipe  in  the  cistern,  is  placed  a  stop  cock, 
which  is  worked  by  a  lever,  at  the  extremity  of  which  there  is 
a  large  hollow  metal  ball,  which  is  raised  by  its  buoyancy  with 
the  surface  of  the  liquid,  and  falls  by  its  weight  when  the  sur- 
face descends.  The  cock  is  thus  closed  when  the  surface  rises 
to  a  certain  height,  and  stops  the  supply  of  water  ;  but  when 
the  surface  falls  the  cock  is  again  opened,  and  water  is  ad- 
mitted. 

Many  contrivances,  upon  this  principle,  have  been  suggested 
for  raising  sunken  vessels.  Hollow  boxes  made  water-tight, 
and  including  only  air,  may  be  carried  to  the  bottom  by  heavy 
weights  attached  to  them.  The  boxes  being  secured  to  the 
vessels  to  be  raised,  the  weights  which  sunk  them  may  then  be 
detached.  If  such  a  number  of  these  boxes  be  attached  to  the 
vessel  as  will  displace  more  water  than  is  equal  in  weight  to 
the  vessel  to  be  raised,  and  the  boxes  themselves,  the  whole 
will  float  to  the  surface. 

A  machine  upon  the  same  principle,  called  the  camel,  for  lift- 
ing vessels  over  shoals,  is  the  invention  of  a  burgomaster  of 
Amsterdam  named  Bakker.  In  the  Zuyder  Zee,  opposite  the 
mouth  of  the  river  Y,  there  are  two  sand  banks,  between  which 
there  is  a  shallow  passage,  impassable  to  vessels  of  large  size. 
It  was  the  practice  for  such  vessels  to  take  in  their  cargo  after 
they  had  passed  beyond  this  strait ;  but  the  accumulation  of 
sand  became  at  last  so  considerable,  that  some  means  were 
necessary  to  transport  the  vessels  themselves  over  this  obstacle. 
In  1672,  large  chests,  filled  with  water,  were  fastened  to  the 
bottom  of  the  vessel ;  the  water  was  subsequently  pumped  out 
of  these,  so  that  they  acquired  a  buoyancy  or  upward  force 
equal  to  the  weight  of  the  water  discharged :  the  ships  were 
thus  raised  and  enabled  to  pass  the  shalloAv.  A  similar  contri- 
vance had  been  previously  used  at  Rome  by  a  Dutch  engineer 
named  Meyer,  but  not  so  complete  or  effectual  a  one  as  that  of 
Bakker.* 

The  camel,  of  which  we  have  just  explained  the  original 
idea,  consists  of  two  large  hollow  chests,  so  constructed  as  to 
extend  along  the  sides  of  a  vessel,  and  shaped  on  one  side  so 
as  to  lie  close  to  her  sides,  being  square  upon  the  outside. 
Being  filled  with  water,  they  sink,  and  are,  without  difficulty, 
brought  close  to  the  sides  of  the  vessel,  to  which  they  are  at- 
tached by  ropes  which  pass  round  each  of  them  and  under  the 
keel ;  the  water  is  then  pumped  out,  and  the  buoyancy  of  the 
chests  raises  the  ship  in  the  water  so  as  to  enable  it  to  float  over 
a  shoal.  An  East  Indiaman  that  drew  fifteen  feet  of  watei; 
was  so  much  elevated  by  means  of  this  machine,  that  it  only 

*  Prewster'3  Encyclopedia,  v.  296. 


CHAP.    V.  *  LIFE-PRESERVERS.  79 

drew  eleven  feet ;  and  the  largest  ships  of  war  in  the  Dutch 
service,  of  from  90  to  100  guns,  were  always  enabled  to  sur- 
mount the  different  sand-banks  of  the  Zuyder  Zee.  Such  ma- 
chines are  likewise  used  in  Venice  and  in  Russia. 

Life-preservers,  provided  in  case  of  accident  at  sea,  are  con- 
structed upon  the  same  principle.  A  hose,  or  flexible  tube,  is 
composed  of  a  cloth  prepared  by  a  solution  of  caoutchouc  or 
India  rubber,  by  which  it  becomes  impervious  to  air  or  water, 
and  which  is  also  insoluble  in  water.  It  is  made  of  such  a 
length,  that  it  may  surround  the  waist  and  be  secured  by  a 
buckle  in  front :  a  mouthpiece  and  valve  are  provided  at  one 
extremity  of  the  tube,  through  which  it  may  be  inflated.  When 
thus  filled  with  air,  it  becomes  light  when  compared  with  its 
own  bulk  of  water ;  and,  when  surrounding  the  waist,  it  gives 
the  body  such  buoyancy  that  the  upper  part  of  the  person  will 
continually  be  kept  above  the  water. 

The  benefit  of  this  contrivance  in  case  of  accidents  at  sea, 
and  more  especially  when,  as  usually  happens,  they  occur  near 
the  shore,  might  be  rendered  much  more  extensive.  A  long 
hose  of  water-proof  cloth  might  be  constructed,  of  such  a  mag- 
nitude as,  when  inflated,  it  would  have  sufficient  buoyancy  to 
sustain  a  considerable  number  of  persons  ;  straps  might  be 
attached  to  it  at  proper  intervals,  to  be  secured  round  the  waists 
of  those  whom  it  was  necessary  to  support.  Such  an  apparatus, 
when  not  inflated,  might  be  folded  in  a  very  small  bulk ;  and  a 
sufficient  number  of  them  to  save  the  crew  or  passengers  of  any 
vessel  would  neither  be  expensive  to  construct  nor  inconvenient 
to  carry;.  With  such  aid  it  would  be  possible  for  the  ordinary 
boats,  with  which  vessels  are  always  provided,  to  tow  the  crew 
and  passengers  to  shore. 

It  would  be  advisable  to  divide  a  large  hose  for  such  a  pur- 
pose, into  a  number  of  separate  air  cells,  to  provide  against 
the  accidental  rupture  of  any  part  of  it.  Such  an  accident 
would  thus  be  productive  of  no  injury,  as  it  would  allow  the  air 
only  to  escape  from  one  cell. 

(63.)  The  weight  of  the  human  body  is  very  nearly  equal  to 
that  of  its  own  bulk  of  water  ;  its  magnitude,  however,  is  sub- 
ject to  a  small  variation,  caused  by  the  action  of  breathing : 
when  the  lungs  are  inflated,  the  volume  of  the  body  is  greater 
than  after  they  collapse.  It  is  true  that  in  this  case  the  weight 
of  th«  body  as  well  as  its  magnitude,  strictly  speaking,  under- 
goes an  increase  ;  but  the  change  of  weight  is  comparatively 
small,  being  that  of  a  few  grains  of  air,  which  are  alternately 
inspired  and  breathed  out.  The  change  of  volume  produces, 
however,  a  sensible  effect  when  the  body  is  immersed  in  tho 
liquid. 

When  the  chest  is  inflated  with  air  by  drawing  in  the  breath, 


80 


A    TREATISE    ON   HYDROSTATICS.  CHAP.    V. 


the  body  is  somewhat  lighter  than  its  own  bulk  of  water  •  and 
t  it  be  immersed  in  that  liquid,  it  will  displace  its  own  weight 
•re  total  immersion  takes  place.     If  the  head  be  presented 
upwards  and  inclined  backwards,  so  as  to  keep  the  mouth  an* 
nose  in  the  highest  possible  position  relatively  to  the  remainde, 
of  the  body,  a  person  may  float  with  about  half  the  head  above 
water  when  the  chest  is  filled  with  air  ;  but  when  he  breathes 
out,  his  lungs  collapse,  and  the  bulk  of  his  chest  is  diminished  • 
his  weight,  however,  remaining  the  same,  he  must  sink  deeper 
in  order  to  displace  his  own  weight  of  water.     A  living  body 
floating  on  water  is,  therefore,  in  a  state  of  continual  oscillation 
alternately  rising  and  sinking :  this  effect  is  increased  by  the' 
inertia  of  the  body ;  for  when  it  descends  it  will  not  cease  to 
sink  exactly  at  that  depth  at  which  it  displaces  its  own  weight 
of  water,  but  it  will  continue  to  move  with  the  velocity  it  has 
acquired,*  until  the  increasing  weight  of  the  water  displaced 
forces  it  to  return  upwards  :  its  alternate  ascent  is  similarly  in- 
creased.    This  effect  may  be  observed  by  pressing  a  piece  of 
cork  m  water  to  a  greater  depth  than  that  at  which  it  naturally 
floats ;  an  oscillation  will  ensue  which  will  continue  for  some 
time. 

Hence  arises  one  of  the  difficulties  which  are  found  in  float- 
ing on  water ;  for,  in  the  alternate  sinking  of  the  body  the 
mouth  and  nostrils  may  be  so  choked  as  to  intercept  the  breath- 
ing :  a  slight  action  of  the  hands  or  feet  is  therefore  necessary 
to  resist  the  tendency  to  sink  after  each  expiration  from  the 
chest. 

The  lighter  the  body  is  in  relation  to  its  magnitude,  the  more 
easily  will  it  float,  and  a  greater  portion  of  the  head  will  remain 
above  the  surface.  As  the  weights  of  all  human  bodies  do  noi 
3ear  the  same  proportion  to  their  bulk,  the  skill  of  the  swimmer 
is  not  always  to  be  estimated  by  his  success  :  some  of  the  con- 
stituent parts  of  the  human  body  are  heavier,  while  others  are 
lighter,  bulk  for  bulk,  than  water.  Those  persons  in  whom  the 
quantity  of  the  latter  bears  a  greater  proportion  to  the  former 
will  swim  with  a  proportionate  facility. 

Sea  water  has  a  greater  buoyancy  than  fresh  water,  beino- 
latively  heavier ;  and  hence  it  is  commonly  said  to  be  much 
easier  to  swim  in  the  sea  than  in  a  river :  this  effect,  however 
appears  to  be  greatly  exaggerated.  A  cubic  foot  of  fresh  water 
weighs  about  1000  ounces ;  and  the  same  bulk  of  sea  water 
weighs  1028  ounces :  the  weight,  therefore,  of  the  latter  ex- 
ceeds the  former  by  only  28  parts  in  10CO.  The  force  exerted 
by  sea  water  to  support  the  body  exceeds  that  exerted  by  fresh 


nt  which  it  dis- 


*  The  velocity  is  variable;  after  the  body  arrives  at  the  clrnth 
at  a  n'n-f8  °W"  *We-ght  of  water>  its  velocity  is  continually  diminished,  though  not 
a  uniform  rate,  in  conscrjusnce  of  the  increase  of  the  upward  pressure.— AM  ED 


CHAP.    V.  FLOATING.  81 

water  by  about  one  thirty-sixth  part  of  the  whole  force  of  the 
latter.* 

It  has  been  proved  that  in  whatever  position  a  body  floats  on 
a  liquid,  the  same  bulk  must  be  immersed ;  it  follows,  therefore, 
that  if  a  person  floating  raise  his  hand  above  the  surta.ee  of  the 
water,  an  equal  portion  of  his  head  must  sink.  Hence  the  dan- 
ger arising  to  persons  drowning  is  increased  by  the  involuntary 
effort  by  which  they  stretch  out  their  arms. 

(64.)  The  bodies  of  some  animals  are  much  lighter  than  their 
own  bulk  of  water.  Many  species  of  birds,  such  as  ducks, 
geese,  swans,  and  water  fowl  generally,  present  examples  of 
this.  The  feathers  with  which  they  are  covered  contribute 
much  to  their  buoyancy  ;  and,  in  many  instances,  a  very  small 
portion  of  their  body  will  displace  a  quantity  of  water  equal  to 
their  weight. 

Fishes  have  a  power  of  changing  their  bulk  by  the  distension 
of  an  air  vessel  with  which  they  are  provided  ;  they  can  thus 
at  will  displace  a  greater  or  lesser  quantity  of  water.  When 
they  enlarge  their  bulk,  so  as  to  displace  more  water  than  their 
oAvn  weight,  they  rise  to  the  surface  ;  and  when,  on  the  other 
hand,  they  contract  their  dimensions,  so  as  to  displace  less 
water  than  their  own  weight,  they  sink  to  the  bottom. 

When  a  human  body  is  first  drowned,  the  air  being  ex- 
pelled from  the  lungs,  it  is  heavier,  bulk  for  bulk,  than  water ; 
and,  therefore,  remains  at  the  bottom.  The  process  of  decom- 
position subsequently  produces  gases,  by  which  the  body  is 
swelled  and  increased  in  bulk  so  much,  that  it  displaces  more 
water  than  is  equal  to  its  own  weight,  and  therefore  rises  to 
the  surface.  When  the  vessels,  containing  the  gases  thus 

*  We  are  not,  however,  to  infer,  that  it  requires  only  one  thirty-sixth  part  lesa 
force  to  sustain  the  body  in  sea  water  than  in  fresh  water.  For  this  force  is,  in 
either  case,  equal  to  the  difference  between  the  weight  of  the  body  and  that  of  an 
equal  bulk  of  the  fluid,  and  this  difference  being  small,  the  proportion  or  (more 
properly)  ratio,  in  which  it  is  diminished,  when  the  body  is  transferred  from  fresh 
to  salt  water,  is  much  greater  than  that  in  which  the  weight  of  a  given  bulk  of  the 
fluid  is  increased.  If  we  suppose  the  weight  of  the  body  to  be  190  Ibs.,  and 
that  of  its  own  bulk  of  fresh  water  180  Ibs.,  the  weight  of  the  same  bulk  of  sea 
water,  being  one  thirty-sixth  part  greater,  would  be  185,  and  it  would  require  a 
force  of  10  Ibs.  to  sustain  the  body  in  fresh  water,  and  only  5  Ibs.  in  sea  water.  If 
the  body  is  still  heavier  compared  with  its  bulk  of  water,  the  force  required  to 
sustain  it  in  sea  water,  compared  with  that  in  fresh  water,  will  be  still  less.  We 
have  as  yet  supposed  the  human  body  to  be  heavier  than  either  fluid.  If  it  be 
lighter  than  either  salt  or  fresh  water,  as  Dr.  Franklin  and  others  have  ascertained 
it  to  be  in  many  cases,  even  after  an  ordinary  expiration  of  the  air  ;  then  it  will 
require  no  force  to  sustain  it,  but  only  the  presence  of  mind  necessary  to  direct 
the  face  upwards,  and  to  avoid  struggling,  (allowing  the  lower  parts  of  the  body 
to  sink  gradually  till  it  comes  into  a  vertical  position  ;)  and  to  avoid,  both  in  breath- 
ing and  speaking,  those  violent  and  long-continued  expirations,  which  occasion  a 
greater  exhaustion  of  the  chest  than  occurs  in  an  easy  and  natural  respiration  ; 
and  lastly,  incase  of  an  accidental  immersion  of  the  face,  to  refrain  from  any  at- 
tempt at  breathing  until  the  mouth  or  nose  shall  have  risen  again  above  the  sur- 
face. An  observance  of  these  rules  might  save  many  lives. — AM.  ED. 


82  A    TREATISE    ON    HYDROSTATICS.  CHAP.    V. 

generated,  burst,  the  body  will  again  contract  its  dimensions 
and  sink. 

(65.)  Philosophical  toys  are  constructed  on  this  principle.  A 
small  glass  vessel  is  constructed  in  the  form  of  a  balloon,  which 
is  hollow,  and  the  lower  part  of  which  is  open ;  it  is  immersed 
in  water  with  its  mouth  downwards,  so  that  the  air  included 
within  prevents  the  water  entering  beyond  a  certain  point. 
This  balloon  is  placed  floating  on  the  surface  of  water  contain- 
ed in  a  deep  glass  jar  filled  nearly  to  the  top  ;  a  bladder  is  tied 
on  the  top,  so  as  to  confine  a  small  quantity  of  air  between  it 
and  the  surface  of  the  water  in  the  jar.  A  pressure  being  ex- 
cited by  the  hand  on  the  bladder,  is  transmitted  by  the  air  under 
the  bladder  to  the  water,  and  the  water  again  transmits  it  to 
the  air  included  in  the  balloon ;  this  air  being  elastic,  yields 
to  the  pressure  and  contracts  its  dimensions,  allowing  a  greater 
quantity  of  water  to  enter  the  balloon :  the  balloon  thus  displaces 
a  less  quantity  of  water,  while  its  own  weight,  including  the 
air  in  it,  remains  unaltered.  At  length  the  water  it  displaces 
is  less  than  its  own  weight,  and  it  sinks  slowly  to  the  bottom 
of  the  jar.  When  the  bladder  is  relieved  from  the  pressure, 
the  air  in  the  balloon  again  expands,  the  water  displaced  by  it 
increases,  and  it  slowly  ascends  to  the  surface. 

A  solid  having  air  enclosed,  which  is  exposed  to  the  pressure 
of  the  liquid  in  which  it  is  immersed,  may  arise  to  the  surface 
if  it  be  immersed  only  to  a  certain  depth ;  but  if  it  be  immersed 
to  such  a  depth  that  the  hydrostatic  pressure  of  the^  surrounding 
liquid  so  condenses  the-  air  within  that  the  solid  displaces  a  less 
quantity  of  liquid  than  its  own  weight,  it  can  no  longer  rise. 
A  diver  who  plunges  in  the  sea  is  lighter  when  he  enters  than 
his  own  bulk  of  water ;  but  if  he  proceed  to  a  certain  depth,  his 
dimensions  will  be  so  contracted  by  the  pressure  of  the  sea,  that 
he  will  displace  a  less  quantity  of  water  than  his  own  weight, 
and,  therefore,  cannot  rise  by  mere  buoyancy,  but  must  ascend 
by  the  exertion  of  his  limbs,  swimming/as  it  were,  upwards. 

It  is  known  that  in  the  process  of  congelation,  water  under- 
goes a  considerable  increase  of  bulk  ;  thus  a  quantity  of  water, 
which  at  the  temperature  of  40°  measures  a  cubic  inch,  will 
have  a  greater  magnitude  when  it  assumes  the  form  of  ice  at 
the  temperature  of  32°.  Consequently  ice  is,  bulk  for  bulk, 
lighter  than  water.  Hence  it  is  that  ice  is  always  observed  to 
collect  and  float  at  the  surface. 

A  remarkable  effect  produced  by  the  buoyancy  of  ice  in  water 
is  observable  in  some  of  the  great  rivers  in  America.  Ice  col- 
lects round  stones  at  the  bottom  of  the  river,  and  it  is  sometimes 
formed  in  such  a  quantity  that  the  upward  pressure  by  its 
buoyancy  exceeds  the  weight  of  the  stone  round  which  it  is 


CHAP.    VI.       LIGHTER    LIQUIDS    FLOAT    ON    HEAVIER.  83 

collected ;  consequently  it  raises  the  stone  to  the  surface. 
Large  masses  of  stone  and  ice  are  thus  observed  floating  dow> 
the  river  to  considerable  distances  from  the  places  of  then 
formation. 


CHAP.  VI. 

OF  DIFFERENT  LIQUIDS  IN  COMMUNICATING  VESSELS. 

LIGHTER  LIQUIDS  FLOAT  TO  THE  TOP. OIL,  WATER,  AND  MERCU- 
RY.—CREAM  OF  MILK. — INGREDIENTS  OF  THE  BLOOD. — OIL  AND 
SPIRITS. — PROOF  SPIRITS. — WATER  AND  WINE. — WATER  IN  THE 
DEPTHS  OF  A  FROZEN  SEA  LESS  COLD  THAN  AT  THE  SURFACE.— 
A  LIQUID  MAY  BOIL  AT  THE  SURFACE,  WHILE  THE  LOWER  PARTS 

ARE     COLD. — METHOD    OF    APPLYING    HEAT    TO    BOIL    A    LIQUID. 

METHOD  OF  APPLYING  ICE  TO  COOL  WINE.— DIFFERENT  LIQUIDS 
IN  A  BENT  TUBE. — METHOD  OF  RAISING  WATER  BY  IMPREGNATING 
IT  WITH  AIR. 

(66.)  ALL  that  has  been  proved  in  the  previous  chapter  re- 
specting the  ascent  and  descent  of  solids  in  liquids  is  equally 
applicable  to  two  or  more  liquids  in  the  same  vessel.  In  this 
case,  providing  that  no  chemical  combination  takes  place  be- 
tween the  liquids,  the  lighter  will  always  ascend  and  remain 
above  the  heavier.  And  if  more  than  two  liquids  be  contained 
in  the  same  vessel,  they  will  severally  arrange  themselves  in 
the  order  of  their  weights,  the  lighter  being  above  the  heavier. 

If  oil  and  water  be  mixed  by  shaking  them  in  the  same  bot- 
tle, they  will  speedily  separate  when  the  bottle  is  placed  at  rest 
on  the  table.  The  particles  of  the  oil  will  rise,  and  those  of 
the  water  fall,  until  they  are  totally  disengaged  from  one  an- 
other ;  the  water  occupying  the  lower  part  of  the  vessel  and  the 
oil  the  higher.  If  mercury,  which  is  heavier  than  water,  be 
added  to  the  mixture,  it  will  take  the  lowest  place,  leaving  the 
water  immediately  above,  and  the  oil  at  the  top. 

These  effects  are  only  manifestations  of  the  principle  which 
has  been  already  so  fully  explained  in  its  application  to  solids 
immersed  in  liquids.  A  particle  of  a  lighter  liquid  immersed  in 
a  heavier  displaces  a  portion  of  that  heavier  equal  to  its  own 
bulk,  and  it  is  urged  upwards  by  a  force  equal  to  the  difference 
between  its  weight  and  the  weight  of  the  heavier  liquid  which 
it  displaces.  What  is  true  of  one  particle  is  equally  true  of  any 
number ;  and  when  two  liquids  of  different  weights  are  mixed 
together,  we  may  consider  the  particles  of  the  lighter  to  be 
urged  upwards,  by  the  predominating  effort  of  the  heavier  to 
sink  to  the  bottom. 


A    TREATISE    ON    HYDROSTATICS.  CHAP.    VI. 

There  are  numerous  familiar  effects  which  are  manifestations 
of  the  principle  now  explained.  When  a  vessel  of  milk  is  all 
lowed  to  remain  a  certain  time  at  rest,  it  is  observed  that  a 
stratum  of  fluid  will  collect  at  the  surface,  differing  in  many 
qualities  from  that  upon  which  it  rests.  This  is  called  -ream- 
and  the  property  by  which  it  ascends  to  the  surface  is  its  rela- 
ive  levity:  it  is  composed  of  the  lightest  particles  of  the  milk, 
which  are  in  the  first  instance  mixed  generally  in  the  fluid ;  but 
wnich,  when  the  liquid  is  allowed  to  rest,  gradually  rise  through 
it,^and  settle  at  the  surface. 

When  blood  taken  from  an  inflamed  patient  is  suffered  to 
remain  a  sufficient  time  in  a  vessel  at  rest,  it  resolves  itself 
into  three  parts,  which  arrange  themselves  in  the  order  of  their 
weights  one  above  another.  The  heaviest  element,  called  sc- 
rum, settles  at  the  bottom;  above  that  a  lighter  substance 
called  coagulum,  arranges  itself;  and  at  the  top  the  lightest 
component  part,  called  buff,  is  collected. 

If  oil,  which  rises  to  the  surface  of  water,  be  mixed  with  al- 
cohol or  some  other  spirits,  it  will  settle  at  the  bottom  A 
weaker  spirit  is  heavier,  bulk  for  bulk,  than  a  strong  one,  and 
s  strength  may  be  so  far  reduced  that  it  will  no  longer  float 
on  the  surface  of  oil,  but  will  sink  below  it;  this  is  the  test 
which  fixes  the  strength  of  proof-spirit.  All  spirit  which  floats 
upon  oil  is  said  to  be  above  proof. 

As  all  spirits  are  lighter  than  water,  they  will  float  upon  its 
surface  if  they  be  not  mixed  through  it.  But  if  these  liquids 
e  mixed,  chemical  effects  will  ensue,  which  will  resist  that 
separation  which  mechanical  causes  would  produce.  If  a  ves- 
sel be  half  filled  with  water,  and  a  piece  of  paper  be  laid  upon 
its  surface,  and  wine  be  poured  over  the  paper,  on  carefully 
removing  the  paper  so  as  to  produce  the  least  possible  agitation 
in  the  liquids,  the  wine  will  continue  to  occupy  the  upper  part 
of  the  vessel,  and  the  water  the  lower.  But  if,  on  the  other 
hand,  the  vessel  be  first  filled  with  wine,  and  the  water  be 
similarly  poured  over  it,  it  will  immediately  sink  through  the 
wine,  and  the  liquids  will  be  mixed,  their  chemical  affinity  re- 
sisting the  tendency  of  the  wine  to  rise  to  the  top.  By  the 
following  contrivance,  however,  the  wine  and  water  may  be 
made  to  change  places  without  intermixture. 

Fig  48  Let  A  and  B>  /#•  48-> be  two  vessels  connected 

_Jl-_.      by  a  narrow  neck  C.     Let  E  be  a  tube  from  the 

JS      lower  vessel  B  to  the  upper  vessel  A,  and  let  D 

-A-^  j|lp       be  a  tube  from  the  upper  "vessel  A  to  the  lower 

vessel  B,  and  let  all  communication  betAveen  the 

ffj  BL      vessels  except  by  these  tubes  be  stopped.    Let 

B  be  filled  with  water  to  the  neck  C,  and  let  A 

be  filled  with  wine  to  a  level  above  the  mouth  of 


CHAP.  VI.  HEATED   LIQUIDS.  85 

the  tube  E.  The  water  in  the  lower  vessel,  and  the  wine  in 
the  upper  vessel,  will  thus  be  in  contact  in  the  neck  C,  but  they 
will  continue  separate,  the  wine  will  not  descend  into  the  wa- 
ter. The  vessels  being  now  emptied,  let  the  lower  vessel  be 
filled  with  wine  and  the  upper  one  with  water.  The  water 
which  fills  the  upper  vessel,  pressing  on  the  wine  in  the  tube 
D,  will  force  it  down,  and  compel  it  to  ascend  in  E.  The  wine 
in  the  lower  vessel  will  thus  be  gradually  discharged  in  the 
upper,  while  the  water  in  the  upper  will  be  deposited  in  the 
lower.  If  the  lower  part  of  the  vessel  be  concealed  or  formed 
of  any  substance  not  transparent,  such  a  vessel  is  used  as  a  toy, 
by  which  water  is  apparently  converted  into  wine. 

The  fact  that  water  at  temperatures  between  the  freezing 
point  and  40°  is  lighter,  bulk  for  bulk,  than  at  higher  tempera- 
tures, has  been  already  noticed.*  It  follows,  therefore,  that 
water  at  this  temperature  will  float  upon  the  surface  of  water 
at  higher  temperatures.  Hence  it  follows  that  the  water  im- 
mediately beneath  a  sheet  of  ice  floats  above  the  less  cold  water 
which  is  at  greater  depths  ;  and  this  liquid  being  a  bad  conductor 
of  heat,  the  lower  region  of  a  frozen  sea  may  be  at  a  very  mod- 
erate temperature,  while  the  most  intense  cold  prevails  above. 
Animal  life  may  be  thus  preserved  in  the  lower  parts  of  the 
deep,  which  would  be  destroyed  if  the  heat,  thus  confined  there, 
were  permitted  to  escape.  The  lighter  stratum  of  fluid  under 
the  congealed  surface  forms  a  barrier,  in  a  great  degree,  imper- 
vious to  the  heat,  and  thus  preserves  the  marine  animals  which 
are  in  the  lower  parts  of  the  sea. 

If  heat  be  applied  at  or  near  the  surface  of  water  contained 
if.  a  vessel,  the  higher  strata  of  the  liquid  may  be  made  to  boil, 
while  the  lower  parts  retain  their  original  temperature.  For, 
like  all  other  substances,  water  expands  when  heated,  and 
therefore  becomes  lighter  ;  consequently,  the  hot  water  at  the 
surface  will  not  descend  into  the  lower  part  of  the  vessel,  and 
the  imperfect  manner  in  which  the  liquid  conducts  heat  prevents 
the  lower  strata  from  receiving  any  effect  from  the  increased 
temperature  of  the  surface.f 

On  the  other  hand,  if  the  water  in  the  bottom  of  a  vessel  be 
heated,  it  will  be  rendered  lighter  by  expansion  than  the  cold 

^  *  It  is  lighter  than  at  some  higher  temperatures  near  40°,  though  not  lighter 
than  at  all  higher  temperatures.  The  expansion  of  water  whilst  in  the  fluid  state, 
has  been  found  to  be  very  nearly  the  same  for  any  number  of  degrees  below,  as  for 
the  same  number  above,  40°.  Hence,  at  no  temperature  below  40°,  until  the  water 
is  congealed,  will  it  be  as  light,  bulk  for  bulk,  as  water  at  high  temperatures. — 
AM.  ED. 

t  If,  however,  the  water  be  below  40°,  and  the  heat  be  applied  very  gradually,  so 
as  to  elevate  the  temperature  of  the  surface  but  a  few  degrees,  it  is  evident,  from 
the  principles  just  stated,  that  the  water  at  the  surface  will  be  rendered  heavier, 
and  that  an  intermixture  will  take  place  throughout  the  whole  mass  until  its  torn 
pcrature  has  risen  to  40°. — AM.  ED. 

8 


A    TREATISE    ON    HYDROSTATICS.  CHAP.    VI. 

water  which  is  above  it ;  and,  conformably  to  the  principles  al- 
ready explained,  it  will  ascend  through  the  cold  water  above  it 
m  the  same  manner  as  the  particles  of  oil  would  ascend  from 
the  bottom  of  a  vessel  of  water  and  float  at  the  top.  The  lower 
and  higher  strata  thus  interchange  places,  and  the  latter  in  its 
turn  becoming  heated  more  than  the  former  again  interchanges 
places  with  it.  Thus  so  long  as  the  lower  strata  continue  to 
receive  increased  temperature,  a  constant  interchange  of  posi- 
tion will  be  produced  between  the  higher  and  lower  strata  of 
the  liquid :  ascending  and  descending  currents  will  be  constantly 
maintained  until  the  liquid  boil. 

This  effect  may  be  exhibited  in  such  a  manner  as  to  be  easily 
observed.  Let  a  tall  glass  jar  be  filled  with  cold  water,  and  let 
a  small  quantity  of  amber  reduced  to  powder  be  thrown  into  it 
Amber  being  very  nearly  equal  in  weight,  bulk  for  bulk,  to 
water,  the  difference  of  weight  produces  so  slight  a  tendency 
in  it  to  sink,  that  this  tendency  is  overcome  by  the  molecular 
attraction  of  the  water  for  its  particles  ;  it,  therefore,  remains 
suspended  in  the  liquid,  being  mixed  through  every  part  of  it, 
and  is  distinctly  visible  to  the  eye.  Let  the  jar  be  now  im- 
mersed to  a  small  depth  in  a  vessel  of  hot  water,  so  that  the 
lowest  strata  of  water  in  the  jar  may  be  gradually  heated.  The 
water  at  the  bottom  of  the  jar  will  be  observed  continually  to 
ascend,  carrying  up  the  particles  of  amber  with  it,  while  the 
upper  strata  descend.  This  will  be  rendered  visible  by  the 
ascent  and  descent  of  the  particles  of  amber. 

In  like  manner  if  the  jar  be  totally  submerged  in  another 
glass  jar  of  boiling  water,  the  portion  of  water  near  the  surface 
of  the  submerged  jar  will  first  become  heated,  and  will  there- 
fore be  lighter  than  the  water  near  its  centre.  In  this  case  we 
shall  observe  a  current  of  amber  particles  continually  ascending 
near  the  surface  of  the  submerged  jar,  while  a  contrary  current 
is  constantly  maintained  near  its  centre.  The  heated  water 
near  the  surface  thus  continually  interchanges  places  with  the 
colder  water  in  the  centre. 

When  a  liquid  has  attained  a  certain  temperature,  which  is 
always  the  same*  in  the  same  liquid,  but  which  differs  in  dif- 
ferent liquids,  it  will  be  incapable  of  any  further  increase.  If 
the  vessel  which  contains  it  be  exposed  to  fire,  or  any  other 
source  of  increased  heat,  the  effect  produced  upon  the  liquid 
will  not  be  to  make  it  hotter,  but  to  convert  it  into  vapor  or 
steam.  If  the  lowest  stratum,  as  is  usually  the  case,  be  that 

k  The  temperature  at  which  this  takes  place  varies  according  to  some  circum- 
stances, the  most  important  of  which  is  the  degree  of  pressure  on  the  fluid.  It 
will  be  obvious  from  this,  when  the  subject  of  atmospheric  pressure  shall  have 
'een  considered,  that  boiling  water  cannot  always  be  equally  hot.  Its  tempera- 
ture is  found  by  experiment  to  vary  at  the  same  place,  and  to  be  much  lower  on 
the  tops  of  high  mountains  than  at  the  level  of  the  ocean.— AM.  ED. 


CHAP.    VI.  HEATED    LIQUIDS.  87 

which  is  exposed  to  the  fire,  the  water  in  it  will  be  first  con- 
verted into  steam,  which  will  be  produced  in  bubbles  at  the 
bottom  of  the  vessel.  These,  being  many  hundred  times  lighter 
than  the  liquid,  will  rise  with  great  rapidity  to  the  surface,  where 
they  will  escape  into  the  air,  producing  that  agitated  appear- 
ance on  the  surface  of  the  liquid  which  is  called  boiling  or 
ebullition.* 

From  the  above  reasoning  it  will  be  evident,  that,  if  fire  be 
applied  for  a  sufficient  length  of  time  to  the  lowest  part  of  a 
vessel  containing  a  liquid,  the  whole  of  the  liquid  in  the  vessel, 
however  remote  it  may  be  from  the  fire,  will  ultimately  become 
heated  ;  for  the  water  occupying  the  lowest  strata  will  continu- 
ally ascend  by  its  increased  levity,  until  the  whole  mass  of 
liquid  receives  the  highest  temperature  of  which  it  is  capable. 
An  apparatus  for  the  warming  of  houses  is  constructed  on  this 
principle.  A  small  metal  boiler,  made  water  tight,  is  placed 
upon  a  fire  in  the  lowest  part  of  the  building.  A  tube  proceeds 
from  this  vessel,  and  is  carried'  through  all  the  apartments 
which  are  required  to  be  heated,  passing  along  the  walls  in  any 
convenient  direction.  The  tubes  and  boiler  are  completely 
filled  with  water.  A  fire  is  kept  lighted  under  the  boiler  so  as 
to  heat  the  water  which  it  contains.  As  this  becomes  lighter 
by  increased  temperature,  it  ascends  through  the  tubes,  and  is 
replaced  by  the  colder  water  descending ;  and  this  continues 
until  the  water  in  all  the  tubes  is  raised  to  the  boiling  point : 
the  metal  of  the  tubes  becomes  ultimately  heated  to  the  tem- 
perature of  boiling  water,  and  imparts  an  increased  tempera- 
ture to  the  air  which  surrounds  them. 

The  same  tubes  being  furnished  in  proper  places  with  cocks 
will  supply  hot  water  for  baths  and  other  domestic  purposes  in 
every  part  of  the  building. 

The  same  reasoning  which  proves  that  to  heat  a  liquid  the 
source  of  heat  should  be  applied  to  the  lowest  strata,  necessa- 
rily leads  to  the  conclusion,  that  to  cool  a  liquid  the  source  of 
cold  should  be  applied  to  the  highest  strata.  If  the  lowest  part 
of  a  vessel  containing  a  liquid  be  plunged  in  melting  ice,  the 
liquid  near  the  bottom,  imparting  its  heat  to  the  ice,  will  be 
cooled,  and  being  rendered  heavier  than  the  liquid  above,  it 
will  remain  at  the  bottom.  In  this  case  the  only  part  of  the 
vessel  which  will  be  cooled  will  be  the  lower  strata ;  the  upper 
parts  will  maintain  their  former  temperature.  But  if  the  highest 
stratum  of  the  liquid  in  the  vessel  be  surrounded  by  melting 
ice,  it  will  be  first  cooled,  and  being  rendered  thereby  heavier 

*  These  bubbles,  whilst  they  remain  at  the  bottom,  impede  the  entrance  of  the 
heat  into  the  water.  Is  not  a  deficiency  of  upward  pressure,  in  consequence  of 
their  contact  with  the  bottom  of  the  vessel,  one  of  the  causes  which  protract  meir 
etay  at  the  bottom  ?— AM.  Ho. 


I 

88  A    TREATISE    ON    HYDROSTATICS.  CHAP.  VI. 

\ 

will  sink  to  the  bottom,  displacing  the  warmer  liquid  below. 
This  process  will  be  continued  so  long  as  the  highest  stratum 
has  a  temperature  above  that  of  the  cooling  application.* 

Hence  it  appears,  that  when  ice  is  used  to  cool  wine,  it  will 
be  ineffectual  if  it  be  applied,  as  is  frequently  the  case,  only  to 
the  bottom  of  the  bottle  ;  in  that  case  the  only  part  of  the  wine 
which  will  be  cooled  is  that  part  nearest  the  bottom.  As  the 
application  of  ice  to  the  top  of  the  bottle  establishes  two  cur- 
rents, upwards  and  downwards,  the  liquid  will  undergo  an  effect 
in  some  degree  similar  to  that  which  would  be  produced  by 
shaking  the  bottle.  If  there  be  any  deposit  in  the  bottom  whose 
weight,  bulk  for  bulk,  nearly  equals  that  of  the  wine,  such  de- 
posit will  be  mixed  through  the  liquid  as  effectually  as  if  it  had 
been  shaken;  in  such  cases,  therefore,  the  wine  should  be 
transferred  into  a  clean  bottle  before  it  is  cooled. 

(67.)  We  have  shown  that  the  same  liquid,  in  communicating 
vessels,  will  always  stand  at  the  same  level ;  this  property  de- 
pends on  the  circumstance  of  columns  of  equal  heights  having 
equal  weights  :  consequently  it  follows,  that  if  communicating 
vessels  contain  different  liquids,  of  which  equal  columns  have 
different  weights,  they  will  not  stand  to  the  same  level.  The 
vessel  which  contains  the  lighter  liquid  will  have  its  surface  at 
a  greater  height,  because  a  column  of  equivalent  weight  to  the 
heavier  will  necessarily  be  higher  ;  and  not  only  so,  but  higher 
exactly  in  that  proportion  in  which  the  liquid  is  lighter.  This 
will  be  more  clearly  understood  by  the  following  illustration  : — 
Let  B  B',  Jig.  49.,  be  a  horizontal  tube  con- 
nected with  two  upright  tubes,  A  B  and  A'  B', 
and  let  a  stopcock  be  placed  at  B'.  Let  the 
horizontal  tube  B  B'  be  rilled  with  quicksilver, 
and  let  two  liquids  lighter  than  quicksilver,  and 
which,  bulk  for  bulk,  have  different  weights,  be 
poured  into  the  tubes  A  B  and  A'  B'  to  any 
heights  as  C  and  C'.  It  is  evident  that  the 
stopcock  B'  is  pressed  downwards  by  the  weight 
of  the  column  C'  B' :  also  it  appears  that  the  mercury  at  B  is 
pressed  downwards  by  the  weight  of  the  column  C  B  ;  and  this 
pressure  is  transmitted  by  the  mercury  to  the  stopcock  B'.  The 
•  stopcock  is,  therefore,  under  the  effects  of  two  opposite  pres- 
sures, viz.  the  weight  of  the  column  C'  B'  downwards,  and  the 
weight  of  the  column  C  B  upwards.  If  either  of  these  pres- 
sures be  greater  than  the  other,  a  corresponding  motion  would 
take  place  on  opening  the  stopcock  ;  thus,  if  the  weight  of  the 
column  Cf  B'  were  greater  than  that  of  the  column  C  B,  the 

_  *  It  will  be  continued  until  the  whole  mass  of  the  liquid  is  cooled  to  40°  ;  at  this 
time  the  currents  cease.  Hence,  ice  floating  or  resting  on  deep  tranquil  water 
does  not  reduce  the  whole  mass  to  its  own  temperature. — AM.  ED. 


CHAP.    VI.       PRESSURE    OF    DIFFERENT    LIQUIDS. 

mercury  would  be  pressed  towards  B,  and  the  liquid  in  C'  B 
would  enter  the  horizontal  tube.  If,  on  the  contrary,  the  weight 
of  the  column  C  B  were  greater  than  that  of  C'  B',  the  upward 
pressure  at  B'  would  be  greater  than  the  downward  ;  and,  on 
opening  the  stopcock  B',  the  mercury  would  be  pressed  up  the 
tube  B'  A'.  In  order,  therefore,  that  the  liquids  in  the  two 
tubes  should  be  in  equilibrium,  on  opening  the  stopcock  it  is 
necessary  that  the  weights  of  the  columns  in  the  upright  tubes 
should  be  equal ;  in  which  case,  whether  the  stopcock  is  open 
or  closed,  equilibrium  will  be  preserved. 

From  this  conclusion  it  is  apparent,  that  the  surfaces  C  and 
C'  will  not  stand  at  the  same  level  unless  the  liquids  in  the 
upright  tubes  have,  bulk  for  bulk,  the  same  weight ;  for  if  one 
be  lighter  than  the  other,  bulk  for  bulk,  it  will,  in  the  same 
proportion  as  it  is  lighter,  require  a  greater  height  of  column  to 
give  the  same  weight  as  the  heavier  liquid.  Thus,  if  a  pint  of 
the  lighter  liquid  weigh  forty  ounces,  and  a  pint  of  the  heavier 
weigh  fifty  ounces,  it  is  evident  that  a  column  of  the  latter,  for- 
ty inches  in  height,  will  exert  the  same  pressure  as  a  column 
of  the  former  fifty  inches  in  height ;  or  in  general  it  may  be 
stated,  that  the  two  columns  will  exert  equal  pressures,  provid- 
ing that  the  height  of  the  column  of  heavier  liquid  shall  bear, 
to  the  height  of  the  column  of  lighter  liquid,  the  proportion  of 
forty  to  fifty,  or  of  four  to  five. 

The  communicating  vessels  in  this  case  are  represented  as 
tubes  of  equal  magnitudes  ;  but,  by  comparing  the  conclusions 
at  which  we  have  just  arrived  with  the  reasoning  used  in  (38.), 
it  will  be  apparent  that  these  inferences  may  be  generalized  ; 
and  that  liquids,  contained  in  any  communicating  vessels  of 
whatever  shape  or  position,  will,  when  in  equilibrium,  have  their 
surfaces  at  heights  determined  on  the  principles  just  laid  down. 
The  surfaces  of  the  lighter  liquids  will  be  more  elevated  than 
those  of  the  heavier  in  proportion  as  their  weights,  bulk  for 
bulk,  are  less. 

Let  A  B  Cjjlg.  50.,  be  a  bent  tube,  open  at  the  ends  A  and 

Fig.  50. 


C,  and  let  oil  and  water  be  poured  into  it ;  let  S  be  the  surface 
of  the  water  on  which  the  oil  rests,  and  draw  the  horizontal 

8* 


90  A    TREATISE    ON    HYDROSTATICS.  CHAP.    VI. 

line  S  M.  If  the  oil  were  removed  from  the  leg  A  B,  and  the 
water  above  M  also  removed  from  the  leg  C  B,  the  water  be- 
low S  M  in  the  curved  tube  would  remain  in  equilibrium,  since 
the  surfaces  S  M  are  at  the  same  level.  That  this  equilibrium 
may  be  continued  when  the  oil  is  introduced  into  the  leg  A  B, 
and  the  additional  water  into  the  leg  C  B,  the  pressures  which 
these  liquids  excite  at  S  and  M  must  be  equal ;  but  the  pres- 
sure at  S  is  equal  to  the  weight  of  a  column  of  oil,  whose  height 
is  S  N,  and  the  pressure  at  M  is  equal  to  the  weight  of  a  col- 
umn of  water,  whose  height  is  M  P,  as  has  been  proved  in 
(37.)  (38.),  &c.  Hence  the  height  S  N  must  be  greater  than 
the  height  M  P,  in  the  same  proportion  as  water  is  heavier  than 
oil ;  and  a  similar  conclusion  may  be  obtained  with  respect  to 
any  other  liquids. 

The  property  by  which  a  short  column  of  a  heavier  fluid  will 
support  a  long  column  of  a  lighter  one,  has  been  used  by  M. 
Dectot  in  machines  invented  by  him,  called  hydreoles,  for  the 
purpose  of  forcing  water  above  its  original  level.  In  these  ma- 
chines water  is,  by  an  ingenious  contrivance,  mixed  with  air ; 
the  mixture  is  of  course  lighter,  bulk  for  bulk,  than  pure  water, 
and  a  short  column  of  the  latter  will  support  a  long  one  of  the 
former.  There  are  different  methods  of  impregnating  the  liquid 
with  air ;  one  in  particular  is  by  forcing  the  air  into  the  water 
by  a  bellows,  through  a  plate  pierced  with  a  number  of  very 
small  holes,  like  the  cover  of  a  sand  bottle,  or  the  rim  of  a  gas 
burner  ;  the  air  thus  enters  the  water  in  extremely  minute  glob- 
ules, so  that  their  buoyancy  is  insufficient  to  overcome  the 
molecular  force  which  attaches  them  to  the  particles  of  the 
water.  An  upright  tube  containing  the  water  thus  impregnated 
with  air,  communicates  with  a  reservoir  containing  pure  water  ; 
and  the  liquid  hi  this  upright  tube  will  stand  as  much  higher 
than  the  water  in  the  reservoir  as  pure  water  is  heavier  than 
the  water  surcharged  with  air.  The  reservoir  answers  the 
double  purpose  of  supplying  the  water  and  pressing  it  up  in  the 
tube  ;  for,  as  it  passes  from  the  reservoir  to  the  tube,  it  encoun- 
ters the  jets  of  air  which  charge  it. 


CHAP,  VII.  FLOATING  BODIES.  91 


CHAP.   VII. 

EQUILIBRIUM  OF  FLOATING  BODIES. 

CONDITIONS  OF  EQUILIBRIUM.— CASES  OF  STABLE,  INSTABLE,  AND 
NEUTRAL  EQUILIBRIUM. — EXPERIMENTAL  PROOF. — FEAT  OF  WALK- 
ING ON  THE  WATER. — LIFE  PRESERVERS. — STABILITY  OF  SHIPS.*— 

POSITION   OF    CARGO. — BALLAST. DANGER    OF    STANDING     UP     IN    A 

BOAT. — INCLINATION     OF    A    SAILING     VESSEL.— HOW     AVOIDED     IN 
STEAM  VESSELS. 

(68.)  THE  circumstances  under  which  a  solid  will  sink,  rise,  or 
"be  suspended  in  a  liquid,  have  been  fully  explained  in  chap.  iv. 
But  these  circumstances  are  insufficient  to  determine  the  exact 
state  of  the  body  with  respect  to  motion  or  rest.  A  body  may 
be  in  equilibrium  with  reference  to  any  perpendicular  motion 
towards  or  from  the  surface  of  the  liquid  ;  that  is,  it  may  nei- 
ther rise  nor  sink,  but  yet  it  may  not  be  in  a  state  of  absolute 
rest.  Again,  to  say  that  a  solid  rises  or  sinks  in  a  liquid  with  a 
certain  force,  does  not  describe  its  state  with  exactness  ;  wh*ile 
it  rises  or  while  it  sinks,  it  may  also  have  motions  of  another 
kind  ;  such  as  motions  in  an  oblique  direction,  or  rotatory  mo- 
tions. To  explain  fully,  therefore,  all  the  conditions  which 
affect  the  state  of  a  solid  immersed,  all  the  particulars  here 
alluded  to  must  be  investigated. 

The  motions  of  which  a  solid  body  is  susceptible  may  in  gen- 
eral be  reduced  to  two,  viz.  progressive  motion,  and  rotatory 
motion.  In  progressive  motion,  all  the  particles  of  the  solid 
are  carried  forward  in  parallel  lines  with  the  same  speed :  in 
rotatory  motion,  the  body  remains  in  the  same  place,  but  turns 
round  some  point  within  it  as  a'  centre.  Let  ABC  T),Jig.  51., 
be  a  solid  body,  and  let  E  F  and  E'  F'  be  the  directions  of  two 
forces  acting  on  it  in  parallel  and  contrary  directions ;  if  these 
two  forces  be  equal,  it  is  evident  that  they  cannot  give  the  body 
any  motion  in  the  direction  E  F  or  in  the  direction  E7  F' ;  for, 
since  the  forces  are  equal,  there  is  no  reason  why  the  body 
should  move  in  the  one  direction  rather  than  the  other.  Such  a 
supposition  would  necessarily  involve  some  distinction  between 
the  two  forces,  whereas  no  such  distinction  exists.  A  force 
of  a  pound  weight  drawing  a  body  towards  the  north,  and 
another  force  of  the  same  weight  drawing  the  same  body  to- 
wards the  south,  evidently  cannot  produce  motion  in  either  of 
these  directions. 

The  effect  of  two  such  forces  as  are  supposed  to  act  in  Jig 


92  A    TREATISE    ON    HYDROSTATICS.         CHAP.    VII. 

51.  will  be  to  give  the  body  a  motion  of  rotation  in  the  direction 
ABCD. 

But  if  the  equal  forces,  instead  of  acting  in  parallel  lines, 
acted  in  the  same  right  line,  and  in  contrary  directions,  then 
they  would  be  mutually  neutralized,  and  the  body  would  be 
kept  at  rest. 

Fig.  51. 


If  the  forces  represented  in  Jig.  51.  were  unequal,  then  the 
body  would  receive  a  progressive  motion  in  the  direction  of  the 
greater  force  ;  but  as  a  consequence  of  the  forces  not  being  in 
the  same  straight  line,  the  body  would  also  receive  a  motion  of 
rotation  in  the  direction  ABCD.  It  would  be  carried  along 
in  the  direction  of  the  prevailing  force,  and  during  its  progress 
it  would  spin  or  revolve. 

If,  however,  the  unequal  and  contrary  forces  act  not  in  parallel 
lines,  but  in  the  same  line,  then  no  rotation  will  ensue,  but  the 
body  will  advance  with  a  progressive  motion  only  according  to 
the  direction  of  the  prevailing  force. 

These  general  mechanical  principles  being  clearly  understood, 
all  the  effects  produced  by  the  immersion  of  a  solid  in  a  liquid 
may  be  rendered  easily  intelligible. 

Let  us  suppose  a  solid  body  of  any  proposed  figure  immersed, 
whether  totally  or  partially,  in  a  liquid. 

A  downward  force  equal  to  the  weight  of  the  solid  is  opposed, 
as  has  been  shown  in  chap,  v.,  by  an  upward  force  equal  to  the 
weight  of  the  liquid  which  the  solid  displaces.  If  either  of 
these  forces  be  greater  than  the  other,  the  body  will  have  a 
tendency  to  rise  or  sink  proportional  to  their  difference  ;  and  if 
they  be  equal,  the  body  will  be  in  equilibrium  as  to  its  ascent 
and  descent  in  a  perpendicular  direction  ;  but  it  still  remains  to 
be  decided,  whether  the  solid  may  not  move  in  the  liquid  with- 
out either  rising  or  sinking. 

To  determine  tlys  it  will  be  necessary  to  ascertain  the  exact 


CHAP.    VII.  FLOATING    BODIES.  93 

directions  of  the  two  forces  downwards  and  upwards  which  act 
upon  the  body. 

The  downward  force  being  the  weight  of  the  solid,  acts  in  a 
direction  pointing  perpendicularly  downwards  from  its  centre 
of  gravity.*  The  direction  of  the  upward  force  is  not,  however, 
so  obvious.  It  is  to  be  considered  that  the  liquid  presses  upon 
the  solid  exactly  in  the  same  manner  as  it  would  press  upon  the 
liquid  whose  place  the  solid  occupies.  Now  it  is  certain,  that 
if  the  space  in  the  liquid,  occupied  by  the  solid,  were  occupied 
by  the  liquid  which  the  solid  has  displaced,  that  liquid  would 
remain  at  rest.  Consequently,  the  downward  pressure  of  that 
liquid  would  be  neutralized  by  the  upward  pressure  of  the  sur- 
rounding liquid.  Therefore,  whatever  that  upward  pressure  be, 
it  must  be  equal  to  the  downward  pressure  of  the  liquid  dis- 
placed by  the  solid,  and  it  must  act  upward  in  the  same  line  as 
the  latter  acts  downward.  But  it  is  easy  to  perceive  that  the 
downward  force  of  the  liquid  displaced  by  the  solid  is  equal  to 
the  weight  of  such  liquid,  and  acts  perpendicularly  downwards 
from  the  centre  of  gravity  of  such  liquid.  Hence,  it  is  evident 
that  the  upward  pressure  which  acts  upon  an  immersed  solid  is 
equal  to  the  weight  of  the  liquid  displaced,  and  that  it  acts  di- 
rectly upwards  in  a  line  from  the  centre  of  gravity  of  the  liquid 
so  displaced. 

This  may  be  also  explained  as  follows  : — Suppose  the  place  ' 
which  the  solid  occupies  in  the  liquid  to  be  filled  by  another 
solid  of  uniform  density,  and  whose  weight  is  equal,  bulk  for 
bulk,  to  that  of  the  liquid.  Such  a  solid,  as  far  as  relates  to 
any  effects  of  weight  or  pressure,  is  equivalent  to  the  liquid 
whose  place  it  occupies  ;  and  as  that  liquid  would  in  its  situa- 
tion remain  at  rest,  it  will  also  remain  at  rest.  Hence,  it  ap- 
pears that  the  upward  pressure  upon  it  must  be  directed  in  the 
same  line  as  that  in  which  its  weight  is  directed  downwards  ; 
but  this  direction  is  that  of  the  perpendicular  line  passing 
through  its  centre  of  gravity.  It  is  evident  that  the  upward 
pressure  against  such  a  solid  must  be  the  same  as  against  any 
other  solid,  the  immersed  part  of  which  occupies  exactly  the 
same  place  ;  and  therefore  it  may  be  inferred  generally,  that 
the  upward  pressure  is  in  the  direction  of  a  line  drawn  directly 
upwards  from  the  centre  of  gravity  of  that  part  of  the  solid 
which  is  immersed,  the  density  of  that  part  being,  like  the  liquid, 
supposed  to  be  uniform. 

Let  A  B  C  D  be  a  solid  immersed  in  a  liquid,  either  partially, 
as  in  Jig.  52.,  or  totally,  as  in  Jig.  53.  Let  E  be  the  centre  of 
gravity  of  the  solid,  and  let  E'  be  the  centre  of  gravity  of  the 
liquid  which  the  solid  displaces.  The  weight  of  the  solid  acts 

*  Ca1!.  Cyc.  Mechanics,  chap.  ix. 


94 


A    TREATISE    ON    HYDROSTATICS. 


CHAP.    VII. 


downwards  in  the  direction  E  F,  and  the  pressure  of  the  sur- 
rounding liquid  acts  upwards  in  the  direction  E'  F'.  These 
two  lines  are  both  perpendicular  to  the  surface  of  the  liquid ; 

Fig.  52. 


they  are  in  the  vertical  direction,  and  are  parallel  to  each  other. 
It  is  evident  from  the  position  of  these  lines,  that  whether  the 
downward  and  upward  forces  be  equal  or  unequal,  they  have  a 

Fig.  53. 


tendency  to  make  the  solid  revolve  or  roll  in  the  direction 
A  D  C  B.  If  the  downward  and  upward  forces  be  unequal,  this 
rolling  motion  will  be  accompanied  by  an  ascent  or  descent  of 
the  solid  in  the  liquid,  according  as  the  upward  or  downward 
force  predominates ;  and  if  they  be  equal,  no  vertical  motion 
will  accompany  the  revolving  one. 

Let  us  now  suppose  the  position  of  the  solid  immersed  to  be 
such,  that  the  points  E  and  E7  shall  be  in  a  straight  line  perpen- 
dicular to  the  surface  of  the  fluid.  In  this  case  the  point  E  may 
either  be  above  E',  as  in  Jig.  54.  and  jig.  55.,  or  below  it.  In 
either  case  the  contrary  forces  upward  and  downward  are  di- 
rectly opposed  to  each  other,  and  have  no  tendency  to  produce 
rotation.  The  solid  will  in  this  case  sink  or  rise  according  aa 
the  upward  or  downward  force  predominates. 


CHAP.    VII.        STABILITY    OF    FLOATING    BODIES. 


95 


If  the  immersion  be  such  in  these  cases  that  the  liquid  dis- 
placed is  equal  in  weight  to  the  solid,  no  motion  whatever  will 
take  place,  and  the  solid  will  be  in  absolute  equilibrium,  neither 
rising,  sinking,  nor  rolling. 

Fig.  54. 


(69.)  A  solid  immersed  in  a  liquid  may  have  several  distinct 
positions  of  equilibrium,  possessing  all  the  various  characters 
of  stability,  instability,  and  indifference,  explained  in  MECHAN- 

Fig.  55. 


ics.*  It  has  been  just  shown  that  whatever  species  of  equilib- 
rium the  body  may  be  in,  it  is  an  indispensable  condition,  that 
the  line  drawn  from  its  centre  of  gravity  to  the  centre  of  gravity 
of  the  liquid  which  it  displaces,  should  be  perpendicular  to  the 
surface  of  the  liquid,  or  in  other  words,  that  it  should  be  in  the 
direction  of  a  plumb  line.  If  this  be  the  case,  the  solid  will 
be  in  equilibrium ;  but  to  distinguish  the  peculiar  kind  of  equi- 
librium in  which  it  will  be  placed,  it  is  necessary  to  attend  to 
other  circumstances.  .  » 

If  the  figure  and  position  of  the  solid  be  such,  that  upon  a 
slight  change  of  position,  by  which  it  still  displaces  its  own 

*  Cab.  Cyc.  Mechanics,  (159.)  et  seq. 


90  A    TREATISE  *ON    HYDROSTATICS.          CHAP.    VII. 

weight  of  fluid,  its  centre  of  gravity  takes  a  higher  position 
than  it  had  when  in  equilibrium,  then  the  equilibrium  will  be 
stable  ;  because  the  centre  of  gravity  having  always  a  tendency 
to  descend  will  return  to  its  former  position,  and  will  oscillate 
from  side  to  side  of  that  position,  until  the  solid,  by  its  friction 
with  the  fluid,  at  length  attain  a  state  of  rest.  Such  is  the 
character  of  stable  equilibrium. 

If  the  position  of  the  solid  in  equilibrium  is  such  that  a  slight 
disturbance,  which  still  causes  it  to  displace  its  own  weight  of 
liquid,  will  make  the  centre  of  gravity  take  a  lower  position, 
the  body  will  not  return  to  its  former  position  of  equilibrium, 
nor  will  it  oscillate  from  side  to  side  of  that  position  as  in  the 
former  case  ;  for  to  do  so  it  would  be  necessary  that  the  centre 
of  gravity  should  ascend,  an  effect  which  is  contrary  to  its  char- 
acteristic property. 

The  centre  of  gravity  will  therefore  continue  to  descend 
until  it  gets  into  another  position,  such  that  the  line  joining  it 
with  the  centre  of  gravity  of  the  fluid  which  it  displaces  shall 
be  perpendicular  to  the  surface  of  the  fluid.  Any  disturbance 
from  this  position  must  necessarily  cause  the  centre  of  gravity 
to  ascend,  and  therefore  this  is  a  position  of  stable  equilibrium. 

The  shape  and  position  of  the  body  may  be  such,  that,  what- 
ever be  the  position  in  which  it  displaces  its  own-  weight  of  the 
liquid,  the  elevation  of  its  centre  of  gravity  will  be  the  same  : 
in  other  words,  any  motion  which  it  may  receive,  allowing  it 
still  to  displace  its  own  weight  of  liquid,  will  cause  its  centre 
of  gravity  to  move  in  a  horizontal  plane,  and,  as  in  this  case  the 
centre  of  gravity  neither  ascends  nor  descends,  it  will  rest  in 
equilibrium  in  all  positions.  Such  is  the  state  of  indifferent  or 
neutral  equilibrium. 

(70.)  If  the  solid  be  totally  immersed,  the  liquid  which  it  dis- 
places will  be  equal,  both  in  shape  and  bulk,  to  the  solid,  and 
the  centre  of  gravity  of  this  liquid  will  therefore  be  the  same 
as  the  centre  of  gravity  of  the  solid,  if  the  latter  have,  like  the 
former,  a  uniform  density ;  but  if  the  solid  be  heavier  in  one 
part  than  in  another,  which  would  be  the  case  if  different  parts 
were  composed  of  different  materials,  then  the  centre  of  gravity 
of  the  solid  will  not  be  in  general  in  the  same  place  in  which 
it  would  be  if  the  solid  were  of  uniform  texture,  and  therefore 
will  not  coincide  with  the  centre  of  gravity  of  the  liquid  dis- 
placed. 

If  the  centre  of  gravity  of  the  solid  have  that  situation  which 
it  would  have  if  the  texture^of  the  solid  were  uniform,  then 
upon  total  immersion  the  points  marked  E  and  E',  injig.  53., 
will  be  one  and  the  same,  and  the  lines  E  F  and  E'  F'  can  never 
be  parallel  to  each  other  whatever  be  the  position  of  the  body 
in  the  liquid,  but  will  always  be  directly  and  immediately  op- 


CHAP.    VII.        STABILITY    OP    FLOAT&G    BODIES.  97 

posed.  Hence  the  downward  and  upward  forces,  the  directions 
of  which  are  expressed  by  those  lines,  can  never  act  in  such  a 
manner  as  to  cause  the  body  to  revolve,  but  can  merely  give  it 
a  tendency  to  ascend  or  descend  in  the  liquid  without  any  other 
change  of  position.  If  in  this  case  the  weight  of  the  solid  be 
equal  to  that  of  its  own  bulk  of  the  liquid,  it  will  be  suspended 
in  equilibrium  in  any  position  whatever  when  it  is  totally  sub- 
merged. In  this  case  the  solid,  when  totally  submerged,  is 
always  in  a  state  of  neutral  equilibrium. 

If  the  centre  of  gravity  of  the  solid  be  not  in  that  situation 
which  it  would  have  if  the  solid  were  of  uniform  texture,  then 
its-  position  will  not  coincide  with  that  of  the  liquid  whose  place 
it  occupies  when  totally  submerged.  If  the  weight  of  the 
solid  be  equal  to  that  of  its  own  bulk  of  the  liquid,  there  are  in 
this  case  only  two  positions  in  which,  when  submerged,  it  will 
be  in  equilibrium.  These  are  the  positions  in  which  the  centre 
of  gravity  of  the  solid  is  immediately  above  and  immediately 
below  the  centre  of  gravity  of  the  liquid  whose  place  it  occu- 
pies. If  the  centre  of  gravity  of  the  solid  be  immediately 
above  that  of  the  liquid  displaced,  it  is  in  the  highest  position 
which  the  circumstances  of  the  case  admit  it  to  have,  and  there- 
fore, the  least  disturbance  must  cause  it  to  descend,  which  it 
will  continue  to  do,  until  it  takes  the  other  extreme  position  in 
which  it  is  immediately  below  the  centre  of  gravity  of  the  liquid 
displaced.  The  former,  therefore,  is  the  position  of  instable 
equilibrium,  and  the  latter,  of  stable  equilibrium. 

(71.)  These  various  effects  of  total  submersion  may  be  easily 
verified  experimentally.  Let  a  hollow  brass  ball  be  provided 
with  a  small  weight  within  it,  movable  by  a  screw,  in  such  a 
manner,  that  the  centre  of  gravity  of  the  ball  may  be  made  at 
pleasure,  either  to  coincide  with  its  centre,  or  to  take  other 
positions  at  any  distance  from  its  centre  ;  and  let  the  weight  of 
the  ball  be  so  adjusted  that  it  shall  be  equal  to  the  weight  of 
the  liquid  which  it  displaces. 

First,  let  the  centre  of  gravity  of  the  ball  be  so  adjusted  as 
to  coincide  with  its  centre.  It  is  evident  that  it  will  thus  have 
the  same  position,  as  the  centre  of  gravity  of  the  liquid  which  it 
will  displace.  If  the  ball  be  now  totally  submerged  in  the  liquid, 
it  will  be  found  that  it  will  rest  in  any  position  whatever,  in 
which  it  is  placed  ;  whatever  point  of  the  ball  be  presented 
downwards  will  remain  so. 

Let  the  screw  be  now  so  adjusted  that  the  centre  of  gravity 
of  the  ball  shall  be  at  some  distance  from  its  centre,  and  let  the 
ball  be  totally  submerged.  It  will  be  found,  if  such  a  position 
be  given  to  the  ball,  that  its  centre  of  gravity  shall  be  immedi- 
ately below  its  centre,  the  ball  will  remain  steady  in  its  posi- 
tion ;  but  if  it  be  placed  with  its  centre,  of  gravity  presented  in 
9 


A    TREATISE    ON    HYDROSTATICS.          CHAP.    VII 

any  direction  sideways,  the  ball  will  turn  on  its  centre,  and  the 
centre  of  gravity  will  fall  towards  that  position  in  which  it  is 
mmediately  under  its  centre,  and  the  body  will  vibrate  until 
s  friction  of  the  fluid  reduces  it  to  a  state  of  rest.     If  the  ball 
be  submerged  in  such  a  position,  that  its  centre  of  gravity  shall 
•e  immediately  above  its  centre,  then  the  ball  will  remain  in 
equilibrium  for  an  instant,  while  it  sustains  no  disturbance  • 
it  its  balance  will  be  tottering  and  instable,  and  will  almost 
immediately  be  lost,  and  the  ball  will  reverse  its  position,  throw- 
ing its  centre  of  gravity  into  the  situation  immediately  opposite 
to  that  in  which  it  was  placed. 

(72.)  But  the  conditions  of  stability  are  of  much  greater  in- 
terest and  practical  importance  in  their  application  to  solids 
which  are  lighter,  bulk  for  bulk,  than  liquids.  In  this  case  the 
degree  of  immersion  which  produces  equilibrium,  is  always 
partial,  and  the  centre  of  gravity  of  the  liquid  displaced  does 
not,  as  in  the  former  case,  coincide  with  the  situation  which  the 
centre  of  gravity  would  have  if  the  texture  of  the  solid  were 
uniform.  Therefore  a  solid  of  uniform  texture,  or  having  its 
mtre  of  gravity  in  the  same  situation  as  one  of  uniform  tex- 
ire,  will  not  float  in  equilibrium  in  every  position.  It  will 
only  be  in  equilibrium  when  the  centre  of  gravity  of  the  liquid 
displaced,  shall  be  either  immediately  above  or  immediately 
below  the  centre  of  gravity  of  the  solid.  In  this  case,  the  situa- 
tion of  the  centre  of  gravity  of  the  liquid  displaced,  will  depend 
on  the  shape  of  the  body,  and  the  part  of  it  which  is  immersed. 
>t  all  the  various  positions  which  can  be  given  to  a  solid 
lighter  than  the  liquid,  in  which  it  will  displace  its  own  bulk  of 
the  liquid,  if  there  be  one  in  which  the  centre  of  gravity  will  be 
lower  than  in  any  of  the  others,  that  one  will  be  a  state  of 
stable  equilibrium,  and  it  will  be  one  which  the  body  will  al- 
ways endeavor  to  attain  whatever  other  position  mav  be 
given  to  it. 

The  shape  of  a  body  may  be  such,  that  in  whatever  position 
it  floats  its  centre  of  gravity  will  be  at  the  same  depth  :  such  a 
ody  is  always  in  a  state  of  neutral  equilibrium  ;  the  least  dis- 
turbing force  will  cause  it  to  change  its  position,  and  it  will  re- 
mam  in  any  new  position  which  may  be  given  to  it. 

Let  the  hollow  brass  ball  already  described,  have  its  weight 
so  adjusted,  that  it  shall  be  lighter,  bulk  for  bulk,  than  water; 
and  let  the  screw  be  moved  until  its  centre  of  gravity  coincides 
with  the  centre  of  the  ball.  From  the  round  form  of  the  ball 
it  is  evident  that,  in  whatever  position  it  is  immersed,  it  will  be 
at  the  same  depth  when  it  has  displaced  its  own  weight  of 
water.  Therefore  its  centre  of  gravity  will  in  this  case  be  at 
the  same  height  or  depth  in  every  possible  position  in  which  it 
can  float.  It  will  be  found,  therefore,  that  it  will  float  on  the 


CHAP.    VII.  WALKING    ON    WATER.  99 

water  steadily  in  any  position  in  which  it  is  placed  ;  it  will  be 
in  a  state  of  neutral  equilibrium. 

Let  the  screw  be  now  so  adjusted  as  to  remove  the  centre 
of  gravity  from  the  centre  of  the  ball,  it  will  be  found  that  it 
will  only  float  steadily  when  the  centre  of  gravity  is  immedi- 
ately below  the  centre  of  the  ball ;  it  will  turn  from  any  other 
position,  and  settle  itself  into  this.  If  it  be  placed  so  that  the 
centre  of  gravity  is  directly  over  the  centre  of  the  ball,  the 
equilibrium  will  be  momentary,  and  upon  the  slightest  change 
of  position  the  ball  will  be  overturned,  and  the  centre  of  gravity 
will  settle  its  elf  Immediately  below  the  centre  of  the  ball. 

(73.)  From  these  observations,  it  will  be  apparent  that  any 
body,  the  parts  of  which  have  different  weights,  will  only  float 
steadily  when  the  heavier  parts  are  immersed  ;  for  the  centre 
of  gravity  is  always  situated  among  these  or  near  them,  and 
therefore,  when  it  has  the  lowest  position,  these  must  also  be 
placed  in  the  lower  parts  of  the  body. 

A  feat  of  dexterity  has  been  exhibited  by  a  person  walking 
on  the  surface  of  water,  having  inflated  bladders,  or  some  other 
bodies  which  are  lighter,  bulk  for  bulk,  than  water,  attached  to 
the  feet.  The  body  of  the  exhibiter  is,  in  this  case,  in  a  state 
of  instable  equilibrium.  His  centre  of  gravity  is  directly  over 
that  of  the  water  which  he  displaces,  and  his  skill  consists  in 
keeping  his  centre  of  gravity  balanced  in  that  position.  This 
feat  may  be  facilitated  by  carrying  a  staff  with  an  inflated  blad- 
der tied  at  the  end  of  it,  by  which  three  points  of  support  may 
be  occasionally  commanded. 

For  the  same  reason  that  buoyant  bodies  are  in  this  case  at- 
tached to  the  feet,  they  are  attached  to  the  waist  in  the  case 
of  life-preservers.  Their  position  and  magnitude  should  always 
be  regulated,  so  that  the  centre  of  gravity  of  the  body*  shall 
be  in  the  lowest  position  when  the  person  is  upright. 

The  weight  of  the  several  component  parts  of  a  ship  and  its 
cargo  should  always  be  so  regulated  that  the  centre  of  gravity 
of  the  whole  should  be  at  the  lowest  possible  point,  when  the 
ship  is  in  the  upright  position. 

Hence  arises  the  necessity  of  stowing  the  heaviest  part  of 
the  cargo  in  the  lowest  possible  position,  and  so  that  its  centre 
of  gravity  shall  be  immediately  over  the  keel ;  in  that  case,  any 
inclination  of  the  vessel  on  either  side  would  cause  the  centre 
of  gravity  to  rise,  to  accomplish  which  would  require  the  ex- 
ertion of  a  force  proportionate  to  the  weight  of  the  vessel,  and 
the  height  through  which  the  centre  of  gravity  would  be  so 
elevated.  When  a  vessel  is  without  a  cargo,  and  empty,  the 
weight  of  the  masts  and  rigging  might  raise  the  centre  of 

*  That  is,  the  common  centre  of  gravity  of  the  human  body,  and  the  buoyant 
substance . — AM.  ED. 


100  A    TREATISE    ON    HYDROSTATICS.          CHAP.    VII. 

gravity  of  the  whole  to  such  a  height,  as  to  render  the  equilib- 
rium instable :  hence,  in  such  cases,  it  becomes  necessary  to 
introduce  heavy  bodies  into  the  lower  part  of  the  vessel,  to 
bring  down  the  centre  of  gravity,  and.  to  give  stability  to  the 
ship.  Hence  bodies  used  for  this  purpose  are  called  ballast. 

The  equilibrium  of  a  boat  may  be  rendered  instable  by  the 
passengers  standing  up  in  it ;  for,  in  this  case,  the  weight  of 
their  bodies  may  place  the  whole  in  the  same  predicament  as 
persons  having  bladders  tied  to  their  feet.  The  slightest  dis- 
turbance, under  such  circumstances,  would  overturn  the  boat. 

If  the  position  of  the  centre  of  gravity  of  a  vessel  and  her 
freight  be  not  directly  over  the  keel,  the  vessel  will  incline  to 
that  side  at  which  the  centre  of  gravity  is  placed  :  and  if  this 
derangement  be  considerable,  danger  may  ensue.  The  rolling 
of  a  vessel  in  a  storm,  may  so  derange  the  position  of  a  loose 
cargo,  that  the  centre  of  gravity  may  be  brought  into  such  a 
situation,  that  the  vessel  may  be  thrown  on  her  beam  ends  and 
irretrievably  lost. 

When  the  centre  of  gravity  is  immediately  over  the  keel,  a 
side  wind  acting  on  the  sails  will  incline  the  vessel  the  oppo- 
site way ;  this  inclination  would  be  much  more  considerable, 
were  it  not  that  the  weight  of  the  vessel,  acting  at  the  centre 
of  gravity,  counteracts  it,  and  has  a  tendency  to  restore  the 
vessel  to  the  upright  position.  The  several  forces  which  main- 
tain the  vessel  in  the  inclined  position  produced  by  a  side  wind, 
may  be  illustrated  as  follows : — Let  A  B,/g-.  56.,  represent  the 

Fig.  56. 


position  of  the  vessel ;  let  S  represent  the  point  at  which  the 
wind  acts  upon  the  sail,  and  let  S  W  represent  the  direction  of 
the  wind :  let  E  be  the  centre  of  gravity  of  the  vessel  and  her 
cargo,  and  let  E  F  be  the  direction  in  which  her  weight  acts. 

Let  C  be  the  centre  of  gravity  of  the  water  which  the  vessel 
displaces,  and  E'  F'  the  direction  of  the  upward  pressure.  If 
the  effect  of  the  upward  and  downward  forces  at  E  and  E7,  be 


CHAP.    VII. 


POSITION    OF    A    SHIP.  101 


considered  for  a  moment,  it  will  be  perceived  that  they  have  a 
tendency  to  incline  the  vessel  to  the  side  opposite  to  that  to- 
wards which  it  is  inclined  by  the  wind.  By  the  principles  of 
the  resolution  of  force  established  in  MECHANICS,*  the  force 
S  W  may  be  replaced  by  three  others,  two  of  which  being  equal, 
and  directly  opposed  to  the  downward  and  upward  forces  at  E 
and  E',  neutralize  them ;  and  the  third,  acting  parallel  to  S  W, 
merely  carries  the  vessel  sideways  perpendicular  to  its  keel, 
producing  what  is  called  lee-way. 

In  sailing  vessels,  this  sideward  inclination  is  a  matter  of 
comparatively  slight  importance,  inasmuch  as  it  does  not  dimin- 
ish the  impelling  power  of  the  wind  :  but  in  steam  vessels,  in 
which  sails  are  occasionally  used,  it  is  attended  with  considera- 
ble loss  of  the  impelling  power,  one  of  the  paddle  wheels  being 
lifted  out  of  the  water,  and  the  other  being  almost,  if  not  en- 
tirely, submerged.  The  upright  position  may,  however,  be 
generally  maintained  by  the  due  management  of  movable 
weights  placed  on  the  deck  of  the  vessel.  In  steam  vessels, 
small  carriages  heavily  laden  with  iron,  and  furnished  with 
wheels,  are  usually  placed  on  the  deck,  and  may  be  rolled  from 
side  to  side,  or  placed  in  the  middle,  so  as  to  regulate  the  po- 
sition of  the  centre  of  gravity  according  to  the  way  in  which 
the  vessel  is  affected  by  the  wind.  By  moving  these  carriages 
to  the  side  of  the  vessel  against  which  the  wind  is  directed, 
the  centre  of  gravity  is  moved  from  over  the  keel  towards  that 
side.  Let  E,  J?g,  57.,  represent  the  place  of  the  centre  of  grav- 

Fig.  57. 
JB 


K 


ity  when  over  the  keel,  and  let  G  represent  the  point  to  which 
the  centre  of  gravity  is  transferred  by  moving  the  carriages  to 
the  side  of  the  vessel ;  let  S  be  the  point  where  the  wind  acts 
upon  the  sail  S  W  ;  the  weight  of  the  vessel  acting  at  G,  has  a 
tendency  to  make  it  incline  towards  M ;  and  the  force  of  the 


*  Cab.  Cyc.  Mechanics,  chap.  v. 

9* 


102  A    TREATISE    ON    HYDROSTATICS.       CHAP.    VIII. 

wind,  acting  at  S  in  the  direction  S  W,  has  a  tendency  to  make 
it  incline  towards  L.  These  two  forces  counteract  each  other, 
and  the  vessel  maintains  its  upright  position. 


CHAP.  VIII. 

SPECIFIC  GRAVITIES, 

DIFFERENT  SENSES  OF  THE  TERMS  HEAVY  AND  LIGHT. — "WEIGHT  AB 
SOLUTE  AND  RELATIVE.' — SPECIFIC  GRAVITY. — STANDARD  OF  COM 
PARISON  FOR  SOLIDS  AND  LIQUIDS. — FOR  GASES. — DENSITY. — THE 
IMMERSION  OF  SOLIDS  IN  LIQUIDS  GIVES  THEIR  SPECIFIC  GRAVITIES. 
— METHODS  OF  ASCERTAINING  SPECIFIC  GRAVITIES. — HYDROSTATIC 
BALANCE.-— SIKES;S  HYDROMETER.— NICHQLSON;S  HYDROMETER. — 
DE  PARCIEUX'S  HYDROMETER.— METHOD  OF  DETERMINING  THE 
CONSTITUENT  PARTS  OF  COMPOUND  BODIES. — ALLOYS  OF  METALS. — 
SPIRITS. — ADULTERATION  OF  MILK  AND  OTHER  DOMESTIC  LIQUIDS. 
— HIERO'S  CROWN. — PENETRATION  OF  DIMENSIONS. 

(74.)  IN  the  preceding  chapters,  we  have  had  frequent  occasion 
to  compare  the  weights  of  different  bodies,  bulk  for  bulk  ;  and 
not  only  in  science,  commerce,  and  the  arts,  but  even  in  ordi- 
nary colloquial  intercourse,  bodies  are  denominated  heavier  or 
lighter,  according  as  the  weights  of  the  same  bulk  are  greater 
or  less.  We  say  familiarly  that  lead  is  heavier  than  copper, 
and  that  copper  is  heavier  than  cork ;  yet  it  is  certain  that 
quantities  of  lead,  copper,  and  cork  may  be  taken  which  have 
equal  weights.  Thus,  let  us  suppose  a  pound  of  lead,  a  pour 
of  copper,  and  a  pound  of  cork,  to  be  ascertained  and  set  apa. 
it  is  clear  that  these  have  equal  weights,  and  that  any  two  c 
them,  placed  in  the  dishes  of  a  balance,  would  maintain  equilib- 
rium. Yet  still  we  do  not  cease  to  declare  that  cork  is  lighter 
than  copper,  and  copper  lighter  than  lead.  To  perceive  with 
precision  what  is  meant  in  this  case,  let  us  suppose  parcels  of 
any  three  distinct  substances  placed  before  us,  such  as  quick- 
silver, water,  and  alcohol,  and  let  it  be  proposed  to  ascertain 
which  of  these  liquids  is  the  heaviest :  we  shall  take  any  meas- 
ure of  the  quicksilver,  and,  having  weighed  it,  afterwards  weigh 
the  same  measure  of  the  water  and  of  the  alcohol  successively. 
Having  found  that  the  measure  of  quicksilver  is  heavier  than 
that  of  water,  and  water  than  that  of  alcohol,  we  shall  immedi- 
ately conclude  that  quicksilver  is  a  heavier  liquid  than  water, 
and  that  water  is  a  heavier  liquid  than  alcohol.  We  shall  form 
this  conclusion,  even  though  the  whole  quantity  of  alcohol  un- 
der examination  shall  weigh  more  than  the  quantities  of  the 
water  or  quicksilver. 

It  appears,  therefore,  that  when  the  weights  of  substances 


CHAP.    VIII.  SPECIFIC    GRAVITY.  103 

are  spoken  of  relatively  to  one  another,  without  any  reference 
to  particular  quantities  or  masses  of  them,  the  weights  meant 
to  be  compared  are  those  of  equal  bulks. 

A  substance  is  sometimes  said  to  be  heavy  or  light,  apparent- 
ly without  reference  to  any  other  substance.  Thus  air  is  said 
to  be  a  very  light  substance,  and  gold  a  very  heavy  one  ;  but, 
in  such  cases,  a  comparison  is  tacitly  instituted  between  the 
weights,  bulk  for  bulk,  of  these  substances  and  those  of  the 
bodies  which  most  commonly  fall  under  our  observation.  When 
we  say  that  air  is  light,  we  mean  that  a  certain  bulk  of  air  is 
much  lighter  than  the  same  bulk  of  most  of  the  substances 
which  we  commonly  meet  with  ;  and  when  we  say  that  gold  is 
heavy,  we  mean  that  any  portion  of  that  metal  is  heavier  than 
a  portion  of  the  same  dimensions  of  the  most  ordinary  substances 
that  we  meet  with.  This  familiar  use  of  a  positive  epithet 
to  express  a  comparison  between  any  quality  as  it  exists  in  an 
individual  instance  and  a  similar  quality  as  it  exists  in  the 
average  of  ordinary  examples,  is  very  frequent,  and  not  confin- 
ed to  the  case  just  alluded  to.  We  speak  of  a  very  tall  man 
and  a  very  high  mountain,  meaning  that  the  man  or  mountain 
in  question  have  much  greater  height  than  men  or  mountains 
commonly  have.  A  man  of  twenty  yeais  of  age  is  said  to  be  a 
very  young  man,  while  a  horse  of  twenty  years  of  age  is  de- 
clared to  be  a  very  old  horse,  because  the  average  age  of  man 
is  much  above  twenty,  and  the  average  age  of  horses  below  it, 

From  what  has  been  now  explained,  it  appears  that  the  term 
weight  is  applied  in  two  distinct,  and  sometimes  opposite  senses. 
A  mass  of  cork  may  have  any  assignable  weight,  as  100  tons. 
This  weight  is  truly  said  to  be  considerable,  and  the  mass  is 
correctly  said  to  be  heavy ;  but  yet  the  cork  which  composes 
the  mass  is  said,  with  equal  truth  and  propriety,  to  be  a  light 
substance. 

(75.)  These  two  ways  of  considering  the  weight  of  a  body 
may  be  denominated  absolute  and  relative.  The  absolute  weight 
of  a  body  is  that  of  its  whole  mass,  without  any  reference  to  its 
bulk  ;  the  relative  weight  is  the  weight  of  a  given  magnitude 
of  the  substance  compared  with  the  weight  of  the  same  magni- 
tude of  other  substances.  The  term  weight,  however,  is  com- 
monly used  to  express  absolute  weight,  while  the  relative  weight 
of  a  body  is  called  its  specific  gravity. 

The  origin  of  this  term  is  obvious.  Bodies  which  differ 
in  other  qualities  are  found  also  to  differ  in  the  weights  of 
equal  volumes.  Thus  a  cubic  inch  of  atmospheric  air  has  a 
weight  different  from  a  cubic  inch  of  oxygen,  hydrogen,  or  any 
of  the  other  gases.  The  number  of  grains  in  a  cubic  inch  of 
gold  is  different  from  the  number  of  grains  in  the  cubic  inch  of 
platinum,  silver,  or  any  of  the  other  metals.  A  cubic  inch  of 


104  A   TREATISE    ON    HYDROSTATICS.        CHAP.    VIII. 

water  contains  a  number  of  grains  different  from  a  cubic  inch 
of  sulphuric  acid,  alcohol,  or  other  liquids.  Hence,  it  appears 
that  the  weight  of  a  given  bulk  of  any  substance,  being  differ- 
ent from  the  weight  of  the  same  bulk  of  other  substances,  may 
be  regarded  as  an  index  or  test  of  its  species,  and  by  the  weights 
of  equal  bulks  bodies  may  be  separated  and  arranged  in  species. 
Hence  the  term  specific  weight,  or  specific  gravity. 

(76.)  When  bodies  are  to  be  compared,  in  respect  of  any 
common  quality,  a  standard  of  comparison  becomes  necessary, 
in  order  to  prevent  an  express  reference  to  two  bodies  in  every 
particular  case.  Thus,  if  we  would  express  the  height  of  any 
body  without  some  standard  measure,  we  could  only  do  so  by 
declaring  it  to  be  so  many  times  as  high,  or  bearing  such  a 
proportion  to  the  height  of  some  other  body.  But  a  foot,  or  a 
yard,  being  known  lengths,  it  is  only  necessary  to  state  that  the 
height  of  the  body  is  so  many  feet,  or  so  many  yards.  In  like 
manner,  if  we  would  express  the  specific  gravity  of  lead,  we 
should  state  that  it  had  such  a  proportion  to  the  weight  of  some 
other  body,  the  weight  of  a  certain  bulk  of  which  is  known. 
But  if  one  substance  be  selected,  to  which,  as  to  a  standard,  all 
others  shall  be  referred,  then  the  specific  gravity  of  any  sub- 
stance may  be  expressed  simply  by  a  number  which  has  the 
same  proportion  to  one  or  the  unit  as  the  weight  of  any  bulk  of 
the  substance  in  question  has  to  the  weight  of  an  equal  bulk  of 
the  standard  substance. 

The  body  selected  as  the  standard  or  unit  of  specific  gravity 
should  be  one  easily  obtained,  and  subject  as  little  as  possible 
to  variation  by  change  of  circumstances  or  situation.  For  this 
purpose  water  possesses  many  advantages  ;  but,  in  deciding  the 
state  in  which  it  is  to  be  considered  as  the  standard,  several 
circumstances  must  be  attended  to. 

First,  The  water  must  be  pure,  because  the  admixture  of 
other  substances  will  affect  the  weight  of  a  given  volume  of  it ; 
and  since  at  different  times,  and  in  different  places,  water  may 
have  different  substances  mixed  with  it,  the  standard  would 
vary,  and  therefore  the  specific  gravities  of  substances  ascer- 
tained with  reference  to  it  at  different  times  and  places  would 
not  admit  of  comparison.  Thus,  if  the  proportion  of  the  weight, 
bulk  for  bulk,  of  gold  to  the  weight  of  the  water  of  the  Seine 
were  ascertained  at  Paris,  and  the  weight  of  another  specimen 
of  that  metal  relatively  to  the  water  of  the  Thames  were  ascer- 
tained at  London,  the  specific  gravities  of  the  two  portions  of 
metal  could  not  be  inferred  unless  it  were  previously  known 
that  the  water  of  the  Thames  and  the  water  of  the  Seine  were 
composed  of  the  same  ingredients,  or  if  not,  unless  their  rela- 
tive weights,  bulk  for  bulk,  were  previously  determined.  That 
the  standard  therefore  may  be  invariable,  it  is  necessary  that 


CHAP.    VIII.      STANDARD    OF    SPECIFIC    GRAVITY.  105 

all  substances  which  may  be  combined  with  the  water  shall  be 
extricated. 

Such  heterogeneous  matter  as  may  be  suspended  in  the  liquid 
in  a  solid  state  may  be  disengaged  from  it  by  filtration  ;  that  is, 
by  passing  the  liquid  through  a  solid  substance  whose  pores  are 
smaller  than  the  solid  impurities  to  be  extricated.  If  any  sub- 
stances be  held  in  solution  by  the  water,  or  be  chemically  com- 
bined-with  it,  they  may  be  disengaged  by  distillation ;  that  is, 
by  raising  the  temperature  of  the  liquid  to  a  point  at  which  the 
water  will  pass  off  in  vapor,  leaving  the  other  substances  be- 
hind ;  or,  if  those  other  substances  vaporize  at  a  lower  heat, 
they  Avill  pass  off,  leaving  the  water  behind  :  in  either  case  the 
water  will  be  separated  from  the  other  bodies  with  which  it  is 
combined.  It  is  evident  that  this  latter  process  of  distillation 
also  serves  the  purposes  of  the  former  one  of  filtration. 

Secondly,  The  water  being  thus  obtained  in  its  pure  state, 
and  free  from  admixture  with  any  other  substance,  it  is  to  be 
considered  whether  there  be  any  other  cause  which  can  make 
the  same  bulk  of  the  liquid  weigh  differently  at  different  times 
and  places.  We  have  already  more  than  once  alluded  to  the 
way  by  which  bodies  are  affected  in  changes  of  temperature. 
Every  increase  of  temperature,  in  general,  produces  an  increase 
of  bulk,  and  therefore  causes  a  given  volume,  as  a  cubic  inch, 
to  weigh  less.  Hence,  in  comparing  the  weights,  bulk  for  bulk, 
of  any  substances,  at  different  times  or  places,  with  the  weight 
of  pure  water,  the  results  of  the  investigation  would  not  admit 
of  comparison  unless  the  different  states  of  the  water  with  re- 
spect to  temperature  were  distinctly  known.  In  addition,  there- 
fore, to  the  purity  of  the  water  taken  as  a  standard,  it  is  expe- 
dient that  some  fixed  temperature  be  adopted.  It  has  been  al- 
eady  explained  that  water,  as  it  decreases  in  temperature,  also 
;ontracts  its  dimensions  until  it  attains  the  temperature  of  about 
40°  ;  it  then  again  begins  to  expand :  at  this  temperature  of  40° 
it  is  therefore  in  its  least  dimensions,  and  it  is  known  that  when 
the  water  is  pure,  its  state  at  this  temperature  is  independent 
of  time,  place,  or  other  circumstances ;  it  is  the  same  at  all 
parts  of  the  earth,  and  under  whatever  circumstances  it  may  be 
submitted  to  experiment. 

The  temperature  at  which  pure  water  has  its  dimensions  most 
contracted  is  called  the  state  of  greatest  condensation,  because 
then  the  mass  of  the  liquid  is  reduced  to  the  smallest  possible 
dimensions,  and  its  particles  have  the  greatest  possible  proximity. 

The  weight  of  a  given  bulk  of  distilled  water  in  the  state  of 
greatest  condensation  is,  therefore,  the  standard  of  specific 
gravity.* 

*  This  is  the  best  standard,  though  water  at  the  temperature  of  60°  has  been  mor» 
generally  adopted  by  English  philosophers. — AM.  ED. 


106  A    TREATISE    ON    HYDROSTATICS.          CHAP.    VIII. 

As  it  may  not  be  always  convenient  to  obtain  water  at  this 
temperature,  when  experiments  on  specific  gravity  are  to  be 
made,  numerical  tables  have  been  constructed  expressing  the 
change  of  weight  which  a  given  bulk  of  water  sustains  with 
every  change  of  temperature  ;  so  that  when  the  specific  gravi- 
ty of  any  substance  has  been  found  with  reference  to  water  c.t 
any  proposed  temperature,  it  may  be  reduced  by  a  simple  pro- 
cess of  arithmetic  to  that  which  would  have  resulted,  had  it 
been  compared,  in  the  first  instance,  with  water  at  the  temper- 
ature corresponding  to  the  state  of  greatest  condensation. 

(77.)  If  the  bulk  of  1000  grains  of  pure  water,*  at  the  tem- 
perature of  40°  of  Fahrenheit's  thermometer,  be  ascertained, 
the  number  of  grains  in  the  same  bulk  of  any  other  body  will 
express  its  specific  gravity,  that  of  water  being  1000  ;  or  if  the 
specific  gravity  of  water  be  expressed  by  1,  the  specific  gravity 
of  other  substances  will  be  expressed  by  a  thousandth  part  of 
the  former  numbers.  This  only  requires  that  three  decimal 
places  should  be  taken.  Thus  it  is  found  that  a  volume  of  gold, 
equal  in  bulk  to  1000  grains  of  water,  weighs  19,250  grains. 
Therefore,  if  1000  be  the  specific  gravity  of  water,  19,250  will 
be  that  of  gold ;  or  if  1  be  the  specific  gravity  of  water,  the 
thousandth  part  of  19,250,  which  is  19|,  will  be  the  specific 
gravity  of  gold  ;  which,  expressed  by  the  decimal  notation,  is 
19-250.  A  vessel  which  would  be  filled  by  a  thousand  grains 
of  water  would  contain  19,250  grains  of  gold. 

Bodies  which  exist  in  the  gaseous  or  aeriform  state  are  so 
much  lighter  than  water,  that  it  is  generally  found  expedient  to 
refer  them  to  another  standard,  which  has  a  known  relation  to 
water :  their  specific  gravities  in  relation  to  water  would  be 
expressed  by  numbers  inconveniently  small.  The  standard 
usually  selected  for  bodies  of  this  form  is  atmospheric  air  ;  and 
to  it  the  specific  gravities  of  all  bodies  in  the  gaseous,  aeriform, 
or  vaporous  state  are  referred,  in  the  same  manner  as  bodies  in 
the  solid  or  liquid  are  referred  to  water. 

Observations  respecting  this  standard  of  gaseous  specific 
gravity  may  be  made  similar  to  those  already  given  respecting 
the  liquid  standard ;  but,  in  the  determination  of  the  specific 
gravities  of  gases,  there  are  many  circumstances  to  be  attended 
to  of  too  delicate  and  complicated  a  nature  to  admit  of  being 
explained,  with  any  degree  of  detail,  in  a  treatise  designed  for 
popular  use.  We  shall,  however,  notice  some  of  them  slightly 
as  we  proceed  with  the  subject. 

Atmospheric  air  is  still  more  susceptible  of  changes  in  its 
volume,  arising  from  change  of  temperature,  than  any  bodies  in 
the  liquid  or  solid  form.  It  is,  therefore,  the  more  necessary,  in 

*  It  may  be  convenient  to  remember  that  a  cubic  foot  of  pure  water  at  the  tern 
perature  of  60°  weighs,  with  greet  precision,  1000  ouncea  avoirdupois. 


CHAP.    VIII.  SPECIFIC    GRAVITY    OF    GASES.  107 

fixing  the  standard,  that  the  temperature  should  be  settled. 
The  temperature  which  has  been  selected  for  this  purpose  is 
that  of  melting  ice,  which  corresponds  to  32°,  or  the  freezing 
point,  of  Fahrenheit's  thermometer ;  this  being  a  point  which  is 
independent  of  the  arbitrary  divisions  of  thermometers  in  differ- 
ent countries. 

The  only  cause  which  can  affect  the  dimensions  of  a  given 
weight  of  pure  water  is  the  temperature  to  which  it  is  exposed. 
Although  it  is  not  absolutely  incompressible,  nor  inelastic,  yet 
it  will  undergo  no  sensible  change  of  dimensions  by  any  change 
of  pressure  to  which,  under  ordinary  circumstances,  it  is  liable. 
Therefore,  in  fixing  the  state  in  which  it  is  to  be  regarded  as  a 
standard  of  specific  gravity,  all  variation  of  external  pressure  is 
disregarded.  The  case  is,  however,  altogether  different  with 
atmospheric  air,  which  is  sensibly  affected  in  its  dimensions 
even  by  the  slightest  change  in  external  pressure.  While  the 
temperature  of  this  fluid  remains  the  same,  the  dimensions 
which  a  given  weight  of  it  occupies  may  be  subject  to  changes, 
almost  without  any  assignable  limit,  and  independently  of  any 
change  of  temperature.  To  fix  the  state  of  atmospheric  air,  in 
which  it  shall  be  considered  as  a  standard  of  specific  gravity,  it 
is  necessary  to  declare  the  amount  of  the  pressure  to  which  it 
is  subject.  The  pressure  selected  by  Biot,  who  has  investigat- 
ed the  specific  gravities  of  gases  with  great  success,  is  one 
which  is  equal  to  the  pressure  of  the  atmosphere  when  the  ba- 
rometer stands  at  six  hundredths  of  an  inch  below  30  inches.* 

The  weight  of  atmospheric  air  and  other  gases  is  also  affect- 
ed by  the  quantity  of  moisture  which  they  hold  suspended. 
An  instrument,  called  a  hygrometer,  has  been  contrived  for  the 
purpose  of  showing  the  relative  state  of  gases  with  respect  to 
this  moisture.  A  due  attention  to  the  indications  of  this  instru- 
ment is  therefore  also  necessary  to  settle  the  state  in  which 
atmospheric  air  is  to  be  regarded  as  the  standard. 

The  state  of  the  standard  being  then  settled,  the  dimensions 
of  1000  grains  of  atmospheric  air  are  determined.  The  num- 
ber of  grains,  and  fractions  of  a  grain,  of  any  other  gases  filling 
the  same  dimensions,  will  express  their  specific  gravities,  that 
of  the  standard  being  1000.  In  order  to  ascertain  the  specific 
gravity  of  any  gas  with  reference  to  water,  it  is  only  neces- 
sary to  consider  the  specific  gravity  of  the  standard,  atmospheric 
air,  in  reference  to  water.  A  portion  of  the  former,  equal  in 
bulk  to  1000  grains  of  the  latter,  will  weigh  one  grain  and  22 
hundredth  parts  of  a  grain. 

(78.)  From  all  that  has  been  explained,  there  are  several  in- 
ferences which  may  be  made  respecting  the  relation  between 

*  This  will  be  more  easily  comprehended  afteF  our  treatise  on  Pneumatics  has 
been  studied. 


108  A    TREATISE    ON   HYDROSTATICS.        CHAP.    VIII. 

the  weights  and  bulks  of  bodies,  which  will  be  found  useful  in 
all  investigations  which  relate  to  specific  gravity. 

If  two  bodies  have  equal  magnitudes,  their  absolute  weights 
will  be  in  the  same  proportion  as  their  specific  gravities.  Thus, 
suppose  a  certain  bulk  of  copper  weighs  7600  ounces,  and  the 
same  bulk  of  brass  weighs  7824  ounces,  then  the  specific  grav- 
ities of  the  two  metals  will  be  in  the  proportion  of  these  two 
numbers,  because  both  are  related  to  the  same  standard,  viz. 
water;  and,  in  fact,  the  magnitude  of  1000  grains  of  water 
is  equal  to  that  of  7600  grains  of  copper,  and  to  7824  of  brass. 

If  two  bodies  have  equal  absolute  weights,  then  their  specific 
gravities  will  be  in  what  is  called  the  inverse  proportion  of  their 
magnitudes  ;  that  is,  the  body  which  has  the  greater  magnitude 
will  have  a  specific  gravity  as  much  less  than  the  other  as  its 
magnitude  is  greater.  Suppose  A  and  B  are  two  bodies  of 
equal  weight,  the  dimensions  of  A  being  twice  those  of  B.  If 
A  be  divided  into  two  equal  parts,  each  will  have  a  bulk  equal 
to  that  of  B,  and  therefore  the  specific  gravities  of  the  two 
bodies  will  be  in  the  same  proportion  as  the  weight  of  half  of 
A  is  to  the  weight  of  B.  But  the  weight  of  B  is  equal  to  the 
weight  of  A,  and  therefore  the  specific  gravity  of  A  is  in  the 
same  proportion  to  that  of  B  as  the  weight  of  half  A  is  to  its 
whole  weight.  Hence,  the  specific  gravity  of  A  is  half  the 
specific  gravity  of  B,  while  the  dimensions  of  B  are  half  the  di- 
mensions of  A.  Thus  the  dimensions  and  the  specific  gravities 
of  bodies  are  oppositely  related  when  their  absolute  weights 
are  the  same. 

From  the  two  properties  just  explained,  it  appears  that  the 
specific  gravity  of  bodies  may  be  ascertained  either  by  deter- 
mining the  exact  dimensions  of  quantities  which  have  equal 
weights,  or  the  exact  weights  of  quantities  which  have  equal 
dimensions. 

(79.)  It  has  been  seen  that  the  specific  gravity  of  every  body 
changes  with  its  temperature,  because  the  change  of  tempera- 
ture necessarily  infers  a  change  of  dimensions.  But  an  inquiry 
naturally  presents  itself:  Does  not  the  increase  of  dimension, 
produced  by  imparting  heat  to  a  body,  arise  from  the  body  re- 
ceiving an  additional  quantity  of  matter  insinuated  through  and 
among  its  particles,  so  that  in  its  altered  state  it  ought  to  be 
viewed  not  as  the  original  mass  with  increased  dimensions,  but 
as  a  compound  of  the  original  body,  and  a  new  portion  of  mat- 
ter added  thereto  ?  This  inquiry  is  tantamount  to  the  question, 
whether  the  principle  of  heat  be  material.  Nothing  has  been 
supposed  in  this  case  to  be  imparted  to  the  body  except  heat ; 
and  the  heat  so  imparted  has  at  least  exhibited  one  essential 
quality  of  matter,  viz.  the  occupation  of  space,  since  it  has  forced 
asunder  the  constituent  particles  of  the  original  body,  which 


CHAP.    VIII.  IS    HEAT    MATERIAL! 

it  has  penetrated,  and  compelled  them  to  stand  at  a  greater  dis- 
tance to  make  way  for  its  admission.  It  is  true  that  this  effect 
may  be  imagined  to  be  produced  in  other  ways  beside  supposing 
the  particles  of  heat  to  be  material ;  but,  however  it  be  produced, 
the  fact  is  certain,  that  when  heat  penetrates  the  dimensions  of  •• 
a  body,  or,  if  we  may  be  allowed  the  phrase,  when  it  is  mixed 
with  a  body,  the  dimensions  of  the  compound  suffer  an  increase 
in  the  same  manner  as  the  dimensions  of  any  two  fluids,  as  wa- 
ter and  alcohol  when  mixed  together  are  greater  in  bulk  than 
the  water  was  existing  separately. 

The  question,  whether  the  increase  of  magnitude,  caused  by 
raisino-  the  temperature  of  a  body  arises  from  its  having  receiv- 
ed any  addition  of  a  material  substance  to  its  mass,  can  only 
be  decided  by  previously  fixing  some  one  quality  which  will  be 
regarded  as  inseparable  from  matter,  and  therefore  the  pres- 
ence or  the  absence  of  which  being  ascertained  will  decide  the 
presence  or  the  absence  of  the  additional  portion  of  matter  un- 
der inquiry. 

The  quality  which  seems  best  adapted  for  such  a  test  is  weight ; 
and  the  question,  whether  the  increased  dimensions  of  a  heated 
body  proceeds  from  its  having  received  any  increase  of  ponder- 
able matter,  becomes  one  which  is  to  be  decided  by  direct  ex- 
periment. Experiments  to  ascertain  this  fact  have  been  insti- 
tuted, attended  by  every  circumstance  which  could  contribute 
to  ensure  accurate  results.  The  same  body,  at  different  tem- 
peratures, and  therefore  under  different  dimensions,  has  been 
accurately  weighed,  but  no  change  of  weight  has  been  observ- 
ed. We  are,  therefore,  entitled  to  conclude  that,  whatever  be  the 
nature  of  the  principle  which  gives  increased  dimensions  to  a 
body  whose  temperature  is  raised,  whatever  it  be  which  fills  the 
increased  interstitial  spaces  from  which  its  constituent  particles 
are  expelled,  it  is  not  a  ponderous  substance,— it  is  not  one  on 
which  the  earth  exerts  any  attraction,— it  is  not  one  which  if 
unsupported  would  fall,  or  if  supported  would  produce  any 
pressure  on  that  which  sustains  it. 

It  follows,  then,  that  the  change  produced  in  the  specinc 
gravity  of  a  body,  by  any  change  in  its  temperature,  depends 
solely  upon  the  change  produced  in  its  dimensions,  and  not 
upon  any  change  which  takes  place  in  its  weight.  We  are, 
therefore,  entitled  to  conclude,  that  the  specific  gravity  of  any 
body  at  different  temperatures  is  inversely  as  its  magnitude ; 
that  is,  in  the  same  proportion  as  the  dimensions  of  the  body 
are  increased  by  heat,  in  that  proportion  exactly  is  its  specinc 
gravity  diminished.  .  . 

(80.)  Density  is  the  term  used  to  denote  the  proximity  or 
closeness  of  the  constituent  particles  of  any  body  to  each  other, 
and  the  density  of  a  body  is  said  to  be  uniform  when  its  con- 
10 


110  A    TREATISE    ON    HYDROSTATICS.  CHAP.    VIII. 

stituent  particles  are  uniformly  and  evenly  distributed  through 
its  dimensions,  so  that  the  same  number  of  particles  occupy  the 
same  space  in  every  part  of  its  magnitude.  This  is  the  ordi- 
nary notion  of  density ;  but  it  is  one  which,  strictly  speaking, 
is  unphilosophical,  because  it  is  founded  upon  the  supposed  ex- 
istence of  ultimate  constituent  particles,  or  molecules  of  bodies, 
the  aggregate  of  which  form  their  mass.  However  probable 
the  existence  of  such  molecules  may  be,  they  are  not  within  the 
sphere  of  sensible  observation,  nor  can  their  number  or  magni- 
tude under  any  circumstances  be  ascertained.  In  a  strictly 
scientific  sense,  the  term  density  can  be  regarded  as  scarcely 
different  from  specific  gravity.  A  body  is  more  or  less  dense 
when  a  given  volume  of  it  contains  more  or  less  ponderous  mat- 
ter, and  it  is  uniformly  dense  when  equal  magnitudes  of  it,  how- 
ever small,  in  every  part  of  its  dimensions  have  equal  weights. 
When  any  body  suffers  a  change  of  dimensions,  either  by  ex- 
ternal pressure,  or  by  the  effects  of  heat,  since  it  still  contains 
the  same  quantity  of  ponderable  matter,  its  density  must  be  in- 
creased in  the  same  proportion  as  its  bulk  is  diminished,  or  vice 
versa.  In  whatever  sense  the  term  density  be  used,  this  is  ob- 
vious ;  for  if  it  be  supposed  to  refer  to  constituent  particles,  or 
atoms,  it  is  evident  that  the  same  particles  exist  in  the  different 
states  with  a  greater  or  lesser  quantity  of  space  between  them. 

If  the  term  density  be  applied  to  bodies  of  different  kinds, 
such  as  silver  and  gold,  it  can  only  be  used  with  strict  propriety 
synonymously  with  specific  gravity.  If  it  have  any  reference 
to  the  proximity  of  constituent  particles,  and  in  that  sense  the 
density  of  gold  be  declared  to  have  the  same  proportion  to  that 
of  silver  as  the  weights  of  equal  magnitudes  of  these  metals,  it 
will  be  evidently  implied,  that  the  ultimate  constituent  particles 
of  the  gold  are  equal  in  magnitude  to  those  of  the  silver,  but 
that  nineteen  particles  of  the  former  are  included  within  a  space 
equal  to  that  which  contains  only  ten  particles  of  the  latter ; 
these  numbers  being  taken  to  represent  the  specific  gravities 
of  those  metals.  The  hypothesis  on  which  such  conclusions 
as  this  are  founded  is  not  necessary  in  physical  investigation  ; 
and,  indeed,  the  term  density  is  rarely  used,  except  when  it  is 
applied  to  the  same  body  when  subject  to  a  variation  in  its  di- 
mensicns. 

(81.)  In  the  effects  produced  by  the  immersion  of  solids  in 
liquids,  we  find  many  relations  developed  between  the  weights 
and  bulks  of  the  solids  and  of  the  liquids  in- which  they  are  im- 
mersed. Such  effects,  therefore,  have  a  necessary  connection 
with  the  specific  gravities  of  these  classes  of  bodies  ;  and  when 
properly  examined,  it  will  be  found  that  they  will  lead  directly 
to  practical  L.ethods  of  ascertaining  the  specific  gravities  of 
bodies,  both  in  the  solid  and  liquid  state. 


CHAP.    VIII.  SPECIFIC    GRAVITY.  Ill 

It  has  been  shown  that  a  solid,  heavier,  buiK  for  bulk,  than 
a  liquid,  will  sink  in  the  liquid,  and  that  its  apparent  weight 
when  immersed  Avill  be  less  than  its  true  weight,  by  the  weight 
of  the  liquid  which  it  displaces.  As  the  weight  of  the  solid, 
and  the  weight  which  it  loses  by  immersion,  are  the  weights  of 
equal  magnitudes  of  the  solid  and  liquid,  they  will  be  propor- 
tional to  their  specific  gravities.  Hence  we  infer, 

1 .  That  a  solid  will  sink  in  any  liquid  which  is  specifically 
lighter  than  it. 

2.  That  the  specific  gravity  of  the  solid  bears  to  that  of  the 
liquid  the  same  proportion  as  the  weight  of  the  solid  bears  to 
the  weight  which  it  loses  by  immersion. 

(82.)  If  a  solid  be  lighter,  bulk  for  bulk,  than  a  liquid,  it  will 
float  on  the  surface,  displacing  as  much  liquid  as  is  equal  to  its 
own  weight.  It  has  been  proved  that  when  bodies  have  equal 
weights,  their  specific  gravities  are  in  the  inverse  proportion  of 
their  dimensions.  (78.)  Hence  we  infer, 

1.  That  a  solid  will  float  on  the  surface  of  any  liquid  which 
is  specifically  lighter  than  it. 

2.  That  the  specific  gravity  of  the  solid  bears  to  that  of  the 
liquid  the  same  proportion  as  the  part  of  the  solid  immersed 
boars  to  its  whole  dimensions. 

(83.)  It  has  been  proved  that  if  the  weight  of  a  solid  be  equal, 
bulk  for  bulk,  to  that  of  a  liquid,  it  will  remain  suspended  when 
totally  immersed,  neither  rising  nor  sinking.  Hence  it  appears 
that  this  phenomenon  is  an  indication  that  the  specific  gravities 
of  the  solid  and  liquid  are  equal. 

(84.)  If  the  same  solid  be  successively  immersed  in  different 
liquids  which  are  specifically  lighter  than  it,  the  weights  which 
it  will  lose  by  immersion  in  each  of  them  will  be  the  weights  of 
portions  of  the  several  liquids,  equal  in  bulk  to  the  solid,  and 
therefore  equal  in  bulk  to  each  other.  Thus  if  a  solid,  measur- 
ing a  cubic  inch,  be  successively  immersed  in  water,  sulphuric 
acid,  and  alcohol,  and  the  weights  which  it  loses  in  each  be  ob- 
served, we  shall  obtain  the  weights  of  a  cubic  inch  of  each  of 
these  liquids.  These  weights  will  therefore  be  in  the  propor- 
tion of  the  liquids  severally.  Hence  we  infer, — 

"  That  a  solid,  successively  immersed  in  several  liquids  which 
are  specifically  lighter  than  it,  will  lose  weights  which  are  pro- 
portional to  the  specific  gravities  of  the  several  liquids." 

(85.)  If  a  solid  which  is  lighter,  bulk  for  bulk,  than  several 
liquids,  be  made  to  float  successively  on  their  surfaces,  it  will 
displace  portions  of  them  which  in  each  case  are  equal  to  its 
own  weight,  and  therefore  equal  in  weight  to  each  other.  But 
it  has  been  shown,  that  the  specific  gravities  of  bodies  having 
the  same  weight  are  in  the  inverse  proportion  of  their  rnagni-r 
tudes.  Hence  we  infer, — 


1  12  A    TREATISE    ON    HYDROSTATICS.       CHAP.    VIII. 

"  That  if  the  same  body  float  successively  on  the  surfaces  of 
different  liquids,  the  parts  of  it  which  are  immersed  in  any  two 
of  them  will  be  in  the  inverse  proportion  of  the  specific  gravities 
of  these  liquids." 

Thus,  if  the  liquids  be  sulphuric  acid  and  ether,  the  specific 
gravity  of  the  sulphuric  acid  will  have  the  same  proportion  to 
the  specific  gravity  of  the  ether  as  the  portion  of  the  solid  which 
sinks  in  the  ether  has  to  the  portion  of  it  which  sinks  in  the 
sulphuric  acid. 

(86.)  If  several  solids,  heavier,  bulk  for  bulk,  than  a  liquid, 
be  successively  immersed  in  it,  they  will  sustain  losses  of 
weight  equal  to  the  weight  of  the  liquid  which  they  severally 
displace  ;  consequently  these  losses  will  be  proportional  to  the 
magnitudes  of  the  bodies.  If  the  solids  be  previously  so  ad- 
justed as  to  be  equal  in  weight,  the  specific  gravities  of  any 
two  of  them  will  be  in  the  inverse  proportion  of  their  magni- 
tudes. (78.)  Hence  we  infer, — 

"  That  solids  of  equaj.  weight  immersed  in  the  same  liquid, 
which  is  specifically  lighter  than  them,  lose  weights  which  are 
in  the  inverse  proportion  of  the  specific  gravities." 

Thus,  if  an  ounce  of  silver  and  an  ounce  of  gold  be  immersed 
in  water,  the  weight  lost  by  the  gold  will  bear  the  same  pro- 
portion to  the  weight  lost  by  the  silver,  as  the  specific  gravity 
of  the  silver  bears  to  the  specific  gravity  of  the  gold. 

(87.)  If  several  solids  which  are  lighter,  bulk  for  bulk,  than 
a  liquid,  float  upon  it,  they  will  displace  portions  of  the  liquid 
equal  to  their  own  weight ;  therefore  the  parts  of  them  which 
will  be  immersed  will  be  proportional  to  their  weights.  In  this 
case,  therefore,  if  the  solids  have  equal  magnitudes,  the  parts 
immersed  will  be  in  the  same  proportion  as  their  specific  grav- 
ities. 

(88.)  It  has  been  proved,  that  when  different  liquids  have 
been  placed  in  communicating  vessels  without  mixing  with 
each  other,  their  surfaces  will  rest  at  different  levels,  and  that 
the  heights  of  these  levels  respectively  above  the  surface  at 
which  they  meet  are  greater  in  proportion  as  the  liquids,  bulk 
for  bulk,  are  lighter.  Let  A  B  C,Jig.  58.,  be  a  tube,  as  describ- 


CHAP.    Till.  SPECIFIC    GRAVITY.  113 

ed  in  ((37.),  containing  two  liquids  of  different  weights,  bulk  for 
bulk,  or  of  different  specific  gravities.  It  has  been  already 
proved,  that  when  they  are  at  rest,  the  height  S  N  will  have  the 
same  proportion  to 'the  height  PM  as  the  weight  of  a  given 
bulk  of  the  heavier  liquid  to  a  weight  of  the  same  bulk  of  the 
lighter  ;  hence  it  appears  that  the  heights  of  the  surfaces  O  and 
W,  of  the  two  liquids  above  the  level  of  the  surface  S  at  which 
they  meet,  are  inversely  as  the  specific  gravities  of  the  liquids. 
Thus,  if  S  O  be  oil,  and  S  B  W  be  water,  then  the  specific 
gravity  of  water  will  bear  the  same  proportion  to  the  specific 
gravity  of  oil,  as  the  height  S  N  bears  to  the  height  P  M. 

(89.)  The  methods  of  practically  determining  the  specific 
gravities  of  bodies  depend  upon  the  properties  which  have  been 
just  explained.  The  details  must,  however,  be  different  for 
different  bodies,  and  must  be  suitable  to  their  peculiar  forms  and 
properties. 

The  specific  gravity  of  a  solid  which  is  not  soluble  in  water, 
and  which  is  specifically  heavier  than  that  liquid,  may  be  de- 
termined by  observing  the  weight  which  it  loses  by  immersion. 

The  proportion  which  this  weight  bears  to  the  actual  weight 
of  the  solid,  will  determine  the  specific  gravity. 

Example. — A  piece  of  pure  gold,  cast  and  not  hammered, 
weighing  77  grains,  is  immersed  in  water,  and  is  observed  to 
weigh  only  73  grains  ;  it  therefore  follows,  that  it  displaces  4 
grains  of  water.  The  proportion,  therefore,  of  the  weights  of 
equal  magnitudes  of  the  metal  and  the  water  is  77  to  4,  or  19| 
to  1.  Hence  19,-j;  is  the  specific  gravity  of  gold,  1  expressing 
the  specific  gravity  of  the  standard  liquid. 

Example. — A  piece  of  flint  glass,  weighing  3  ounces,  is  im- 
mersed in  pure  water,  and  observed  to  weigh  only  2  ounces. 
Hence  the  weight  of  the  water  which  is  displaced  is  1  ounce. 
The  specific  gravity  of  the  glass  is  therefore  3. 

(90.)  If  the  solid"  be  soluble  in  water,  this  method  cannot  be 
practised.  In  this  case  the  solid  may  be  defended  from  the 
water  by  a  varnish,  or  a  thin  coating  of  wax,  or  some  other  sub- 
stance not  affected  by  the  water.  The  specific  gravity  of  salts 
and  like  substances  may  be  thus  found.  As,  however,  the  coat- 
ing used  in  this  case  produces  an  increase  of  bulk,  the  solid, 
when  immersed,  will  displace  more  than  its  own  bulk  of  water. 
The  weight  of  the  solid,  if  ascertained  without  the  coating, 
will  bear  a  less  proportion  to  the  loss  of  weight  than  it  doss  to 
its  own  bulk  of  water ;  and  therefore,  the  specific  gravity  ob- 
tained from  such  an  experiment,  would  ia  this  case  be  too 
small.*  But  if  the  weight  of  the  solid  be  ascertained  after  tl\3 


*  This  will  depend  wholly  upon  the  speciric  gravity  of  the  coating.  If 
the  same  as  that  of  water,  it  will  not  affect  the  water  weight  of  the  body  ; 
coating  will  havo  the  name  effect  as  the  water  displaced  by  it ;  and  as  sue! 


If  this  ha 
for  th« 
such  coat- 

10 


114  A    TREATISE    ON    HYDROSTATICS.       CHAP.    VIII. 

coating  is  put  on,  then  the  specific  gravity  which  is  obtained  is 
not  the  specific  gravity  of  the  solid,  but  of  the  solid  and  coating 
together.  Where  great  accuracy  is  not  required,  the  effect 
produced  by  the  coating  may  be  neglected  ;  but  if  the  result  is 
to  be  obtained  with  a  high  degree  of  accuracy,  the  following 
method  is  preferable  : — Find  the  proportion  of  the  specific  grav- 
ity of  the  solid  to  that  of  some  liquid  in  which  it  is  not  soluble, 
and  which  is  specifically  lighter  than  it.  This  may  be  done  by 
observing  the  weight  of  the  solid  and  the  weight  which  it  loses 
by  immersion.  Then  find  the  specific  gravity  of  that  liquid 
with  respect  to  water  by  the  method  Avhich  shall  be  hereafter 
explained. 

If  the  solid  consist  of  many  minute  pieces,  or  be  in  the  form 
of  powder,  a  cup  to  receive  it  ought  to  be  previously  suspended 
in  the  water,  and  accurately  counterpoised. 

(91.)  To  determine  the  specific  gravity  of  a  solid  lighter  than 
water,  let  the  part  immersed  when  it  floats  on  water  be  observ- 
ed, the  proportion  which  this  bears  to  its  whole  magnitude, 
will  be  that  of  its  specific  gravity  to  the  specific  gravity  of 
water.  (82.) 

When  the  solid  floats,  the  proportion  of  the  part  immersed 
to  the  whole  bulk,  may  be  ascertained  in  the  following  manner : 
— Let  the  vessel  which  contains  the  water  have  perpendicular 
sides,  and  be  as  narrow  as  the  magnitude  of  the  solid  will  ad- 
mit. Let  the  point  on  the  vessel  which  marks  the  surface  be- 
fore immersion  be  observed.  Let  the  point  to  which  the  surface 
rises,  when  the  solid  floats,  be  next  observed  ;  and,  finally,  let 
the  solid  be  totally  submerged,  and  the  point  to  which  the  surface 
then  rises  observed.  The  elevations  of  the  surface  produced 
by  the  partial  and  total  submersion,  indicate  the  portions  of  the 
solid  in  each  case  immersed,  and  are  therefore  in  the  ratio  of 
the  specific  gravity  of  the  solid  to  that  of  the  liquid. 

There  is  another  method  of  ascertaining  the  specific  gravity 
of  a  solid  lighter  than  water,  which  ought  to  be  noticed  here. 
Let  the  solid  whose  specific  gravity  is  to  be  ascertained,  be  at- 
tached to  another  which  is  heavier  than  water,  and  of  such  a 
magnitude  that  the  united  weights  of  the  two  will  be  greater 
than  the  weight  of  water  which  they  displace  ;  they  will  there- 
fore sink  when  immersed.  The  weight  of  the  whole  being 
observed,  let  the  weight  which  they  lose  by  immersion  be 
noted  ;  this  will  be  the  weight  of  as  much  water  as  is  equal  in 
magnitude  to  the  united  bulks  of  the  solids.  Let  the  lighter 
solid  be  then  detached,  and  let  the  weight  which  the  heavier 

ing  can  be  easily  prepared,  the  specific  gravity  may  be  accurately  determined  by 
this  method.  But  without  this  precaution,  the  specific  gravity  obtained  by  this 
method  may  be  either  greater  or  less  than  the  true  specific  gravity,  according  as 
the  coating  is  specifically  heavier  or  lighter  than  water. — AM.  ED. 


CHAP.    VIII.  SPECIFIC    GRAVITY.  115 

loses  by  immersion  be  ascertained ;  this  will  be  the  weight  of 
as  much  water  as  is  equal  in  bulk  to  the  heavier  solid.  If  this 
loss  of  weight  be  subtracted  from  the  loss  sustained  by  the 
combined  masses,  the  remainder  will  be  the  weight  of  as  much 
water  as  is  equal  in  bulk  to  the  lighter  solid  :  the  proportion  of 
the  weight  of  the  lighter  solid  to  this  will  determine  its  specific 
gravity. 

(92.)  There  are  several  methods  by  which  the  specific  gravi- 
ties of  liquids  may  be  found. 

If  a  solid  specifically  heavier  than  water,  and  also  specifically 
heavier  than  the  liquid  whose  specific  gravity  is  to  be  determin- 
ed, be  successively  immersed  in  water  and  in  that  liquid,  the 
losses  of  weight  will  be  proportional  to  the  specific  gravities  of 
water  and  the  liquid.  If  the  number  expressing  the  loss  of 
weight  in  the  liquid  be  divided  by  the  number  expressing  the 
loss  of  weight  in  the  water,  the  quotient  will  express  the  spe- 
cific gravity  of  the  liquid. 

Example. — A  piece  of  glass,  immersed  in  sulphuric  acid,  is 
observed  to  lose  3700  grains  of  its  weight.  The  same  solid, 
immersed  in  water,  loses  2000  grains  ;  hence  the  proportion  of 
the  specific  gravity  of  the  sulphuric  acid  to  the  specific  gravity 
of  the  water  is  that  of  37  to  20,  or  of  1850  to  1000 :  therefore 
if  1000  express  the  specific  gravity  of  water,  1850  will  express 
that  of  sulphuric  acid. 

The  specific  gravity  of  a  liquid  may  also  be  found  by  means 
of  a  solid  which  is  specifically  lighter  than  it,  the  same  solid 
being  also  specifically  lighter  than  water.  Let  the  solid  float 
successively  on  the  two  liquids,  and  observe  the  magnitudes 
of  the  parts  immersed,  which  may  be  done  by  observing  the 
change  of  level,  if  the  vessels  containing  the  liquids  have  equal 
bottoms,  and  perpendicular  sides :  the  parts  immersed  will  be 
inversely  as  the  specific  gravities.  (85.)* 

Example. — The  same  solid  floats  successively  on  water  and 
muriatic  acid,  and  the  proportion  of  the  parts  immersed  is  ob- 
served to  be  that  of  10  to  12.  Hence  the  specific  gravity  of 
muriatic  acid  is  12,  that  of  water  being  10. 

(93.)  The  specific  gravities  of  liquids  may  be  ascertained  by 
observing  the  weights  of  two  different  solids  floating  on  their 
surfaces  with  equal  parts  immersed.  In  this  case  the  specific 
gravities  will  be  proportional  to  the  weights  of  the  solids.  But 
perhaps  the  most  direct  method  of  determining  the  specific 
gravities  of  bodies,  as  well  in  the  liquid  as  in  the  gaseous  state, 
is  by  actually  weighing  them  in  a  flask  or  bottle  of  known  mag- 
nitude. Let  such  a  one  be  provided  with  a  stopper  which 

*  Hence  a  ship  will  draw  more  water,  i.  e.  sink  farther,  on  entering  a  fresh 
water  river,  than  when  at  sea.— AM.  ED. 


116 


A    TREATISE    ON    HYDROSTATICS.       CHAP.    VIII. 


nicely  fits  it,  and  let  it  be  filled  with  pure  water  and  weighed, 
and  subsequently  filled  with  any  other  fluid  and  again  weighed ; 
if  the  weight  of  the  flask  be  exactly  known,  the  weight  of  its 
contents  may  in  each  case  be  found.  In  this  manner  the  weight 
of  air  may  be  determined  by  weighing  the  flask  first  filled  with 
air  in  the  ordinary  state,  and,  subsequently,  after  the  air  has 
been  abstracted  from  it,  by  the  air-pump,  an  instrument  which 
will  be  explained  in  a  subsequent  part  of  this  volume.  It  is 
thus  ascertained  that  a  cubic  foot  of  common  atmospheric  air 
weighs  about  527  grains.  This  weight,  however,  fluctuates 
from  causes  already  alluded  to,  and  which  will  hereafter  be 
fully  explained. 

The  empty  flask  may  in  like  manner  be  filled  with  any  other 
species  of  gas,  and  its  weight  relatively  to  that  of  air  may  be  at 
once  determined. 

Instruments  for  the  practiced  measurement  of  specific  gravities. 

(94.)  The  form  and  construction  of  instruments  for  determin- 
ing specific  gravities,  vary  according  to  the  degree  of  accuracy 


J-.J 


required  in  the  results,  and  according  to  the  nature  of  the 
bodies  to  which  they  are  intended  to  be  applied.     In  scientific 


CHAP.    VIII.  HYDROSTATIC    BALANCE.  117 

investigations,  where  the  most  extreme  accuracy  is  sought,  the 
measurement  of  specific  gravities  is  effected  by  a  very  sensible 
balance  furnished  with  certain  additions,  and  mounted  in  a 
manner  from  which  it  has  received  the  name  of  the  hydrostatic 
balance. 

A  front  view  of  the  hydrostatic  balance  is  represented  in  Jig. 
59.,  and  a  side  view  in^g-.  60.  The  corresponding  parts  being 
marked  by  the  same  letters.  A  pillar,  A  B,  fixed  in  a  stand,  C  D, 
supports  the  instrument.  On  the  stand,  placed  in  a  horizontal 
position,  is  a  screw  S,  which,  turns  in  a  fixed  nut  at  T.  This 
screw  is  terminated  by  a  hook,  which  holds  the  loop  of  a  silken 
string,  the  two  parts  of  which,  passing  in  the  grooves  of  wheels 
or  rollers  at  P,  are  carried  from  thence  to  the  top  of  the  pillar 
and  there  pass  over  the  grooves  of  rollers  at  R,  and  their  ex- 
tremities finally  support  a  horizontal  arm  at  E.  To  the  centre 
of  this  arm  e,  a  very  nice  balance  is  suspended :  beneath  the 
beam  of  this  balance  are  placed  rests,  at  m,  so  that  when  the 
beam  is  not  in  use,  by  turning  the  screw  S,  it  will  be  allowed 
to  descend  upon  the  rests  ;  and  the  knife  edges,  on  the  accu- 
racy of  which  the  sensibility  of  the  instrument  depends,  will  be 
relieved  from  pressure.  The  board  G  H,  attached  to  the  pillar 
immediately  below  the  dishes,  is  movable  on  the  pillar,  and 
may  be  fixed  in  any  position  by  means  of  an  adjusting  screw  ; 
also  the  nut  in  which  the  screw  S  turns  is  capable  of  being 
moved  towards  or  from  the  pillar,  so  as  to  raise  or  lower  the 
balance,  in  a  greater  degree  than  would  be  allowed  by  the  play 
of  the  screw  S.  Thus  the  balance  and  all  its  accompaniments 
may  be  raised  or  lowered  at  pleasure.  To  the  centre  of  the 
bottom  of  the  dishes  hooks  c  d  are  attached,  from  which  brass 
wires  are  suspended,  which  pass  freely  through  holes  in  the 
board  G  H.  At  the  lower  extremities  of  these  wires  are  hooks 
h  and  g.  To  the  hook  g-,  a  graduated  rod  g  k  is  suspended, 
which  ^Iso  terminates  in  a  hook  at  k.  The  rod  g  k  bears  a 
scale  of  equal  divisions  ;  an  index  N  O  turns  on  a  rod  M  N 
with  a  horizontal  motion,  and  may  be  applied  to  the  scale  g  k 
or  may  be  removed  at  pleasure  ;  this  index  may  be  also  moved 
upwards  and  downwards  by  means  of  a  screw  M,  which  playa 
in  a  nut  in  the  board  G  H.  A  brass  ball  of  about  |  of  an  inch 
diameter,  is  suspended  from  k,  by  a  brass  wire  k  Z,  of  such  a 
thickness  that  one  inch  of  it  will  displace  half  a  grain  of  water. 
From  the  hook  ht  a  glass  bubble  i  is  suspended  by  a  horse-hair. 
The  brass  ball  and  the  glass  bubble  are  so  adjusted  that  they 
will  hang  about  the  middle  of  the  glass  vessels  X  Y,  in  the 
ordinary  position  of  the  balance.  If  the  dish  c  preponderate, 
the  wire  k  I  will  become  more  immersed ;  and  for  every  inch  it 
sinks,  the  weight  which  draws  down  the  dish  c  will  be  diminish- 
ed to  the  amount  of  half  a  grain,  that  being  the  weight  which 


118 


A    TREATISE    ON    HYDROSTATICS.       CHAP.    VIIL 


an  inch  of  the  wire  loses  by  immersion.  In  like  manner  if  a 
preponderate,  the  wire  k  I  will  be  drawn  up  ;  and  for  every  inch 
which  is  raised  above  the  surface  of  the  water,  an  additional 
weight  of  half  a  grain  will  act  upon  the  dish  c. 

Now  suppose  the  balance  so  adjusted  that  its  tongue  points 
directly  upwards  at  e,  and  that  the  beam  a  6  is  therefore 
horizontal ;  let  the  index  N  O  be  fixed  at  the  middle  point  of 
the  scale  g  k  by  means  of  the  screw  M.  Suppose  the  scale  g  k 
so  divided,  that  its  middle  point  will  be  marked  zero,  or  0  ;  and 
let  each  half  of  it,  being  two  inches  long,  be  divided  into  a 
hundred  equal  parts,  being  numbered  upwards  and  downwards 
from  the  middle  point.  "Let  the  substance  to  be  weighed  be 
placed  in  the  dish  c,  and  let  grain  weights  be  placed  in  the  dish 
</,  until  the  number  of  grains  nearest  to  its  exact  weight  be 
found.  Thus,  suppose  that  it  is  found  that  65  grains  are  insuf- 


:u 


ficient  to  support  the  dish  c,  but  that  66  grains  cause  the  dish  d 
to  preponderate  ;  the  exact  weight  of  the  substance  is,  there- 
fore, more  than  65  grains,  but  less  than  66  grains,  and  the 
object  is  to  determine  by  what  part  of  a  grain  the  true  weight 
exceeds  65  grains.  Weights  to  the  amount  of  65  grains  being 
placed  in  the  dish  </,  the  dish  c  will  slowly  descend  ;  the  wire 
kl  will  consequently  become  more  deeply  immersed  in  the 


CHAP.    VIII.  HYDROSTATIC    BALANCE.  119 

water,  and  for  every  inch  which  sinks,  the  weight  of  c  will  be 
diminished  by  half  a  grain  ;  and  therefore  for  every  division  of 
the  scale  which  passes  the  index  N  O,  the  dish  c  will  lose  weight 
to  the  amount  of  the  hundredth  part  of  a  grain.  When  the  loss 
of  the  weight  thus  sustained  by  the  dish  c  amounts  to  as  many 
hundredth  parts  of  a  grain  as  the  weight  of  the  substance  in 
the  dish  c  exceeds  65  grains,  the  beam  will  remain  in  equilib- 
rium. When  this  takes  place,  therefore,  it  is  only  necessary 
to  observe  the  number  of  the  division  at  which  the  index  N  O 
stands  ;  that  number  will  express  the  hundredth  parts  of  a  grain, 
by  which  the  weight  of  the  substance  in  the  dish  c  exceeds  65 
grains. 

The  weight  might  in  like  manner  be  ascertained  by  placing 
66  grains  in  the  dish  rf,  and  by  causing  it  to  preponderate.  In 
this  case  the  wire  k  I  would  be  drawn  from  the  water,  and  for 
very  division  of  the  scale  g  k  which  would  pass  the  index  N  O, 
the  hundredth  part  of  a  grain  would  be  added  to  the  dish  c  ; 
when  the  dish  d  would  cease  to  descend,  the  number  of  the 
scale  marked  by  the  index  would  express  the  number  of  hun- 
dredth parts  of  a  grain  by  which  the  weight  of  the  substance  in 
the  dish  c  falls  short  of  66  grains. 

The  effect  produced  by  the  immersion  of  the  horse-hair  from 
the  hook  h  is  here  neglected,  because  the  weight  of  the  water, 
which  a  small  portion  of  its  length  displaces,  does  not  exceed  a 
fraction  of  a  grain  much  smaller  than  any  weight  here  taken 
into  account. 

The  weight  of  the  substance  being  thus  ascertained  in  air, 
it  is  next  ascertained  in  a  similar  manner  by  immersion  in  the 
jar  Y,  and  the  loss  of  weight  in  water  is  thus  obtained.  The 
specific  gravity  may  thence  be  inferred  as  explained  in  (89.). 

To  prevent  the  adhesion  of  water  to  the  wire  k  I,  it  is  previ- 
ously oiled,  and  the  oil  gently  wiped  off,  so  as  to  leave  a  thin 
film  covering  the  wire. 

If  the  body  whose  specific  gravity  is  under  investigation  be 
a  liquid,  it  must  be  contained  in  a  glass  vessel,  carefully  stop- 
ped, and  completely  filled.  The  weight  of  the  glass  vessel, 
empty,  is  first  ascertained  by  the  balance,  and  then  its  weight, 
when  filled  with  water,  and  immersed  in  water ;  by  this  means 
the  weight  of  the  glass  will  be  accurately  ascertained,  and  also 
the  weight  which  the  glass  loses  by  immersion  in  water. 
When  the  bottle  is  filled  with  the  liquid,  the  weight  of  the  bot- 
tle is  ascertained,  from  which  the  weight  of  the  glass  being 
subtracted,  leaves  a  remainder  which  is  the  exact  weight  of  the 
liquid.  The  bottle  filled  with  the  liquid  is  now  weighed,  im- 
mersed in  water,  and  the  loss  of  weight  is  observed.  From  this 
loss,  let  the  loss  of  weight  sustained  by  the  glass  alone  be  sub- 
tracted, and  the  remainder  will  be  ths  weight  of  a  quantity  of 


120  A  TREATISE  ON  HYDROSTATICS.        CHAP.  VIII. 

water  equal  in  bulk  to  the  liquid  contained  in  the  bottle.  The 
specific  gravity  of  the  liquid  may  thence  be  immediately  infer- 
red in  the  same  manner  as  if  it  were  a  solid. 

(95.)  The  apparatus  and  processes  which  have  been  just  ex- 
plained are  adapted  to  give  results  of  that  extreme  accuracy 
which  is  necessary  for  the  purposes  of  science.  With  such 
views,  the  complexity  and  expense  of  apparatus,  and  the  time, 
skill,  and  attention  required  for  delicate  manipulations,  are  mat- 
ters of  small  importance  compared  with  the  attainment  of  exact 
results.  But  when  specific  gravities  are  to  be  ascertained  for 
the  ordinary  purposes  of  commerce  or  finance,  means  of  a  more 
simple  character  must  be  resorted  to,  the  use  of  which  is  at- 
tended with  more  expedition,  and  requires  less  skill  in  the 
operator.  In  such  cases  a  degree  of  accuracy,  exceeding  a 
comparatively  wide  limit,  is  altogether  unnecessary  ;  and  even 
though  superior  instruments  were  available,  their  results  would 
not  be  more  useful  than  those  of  a  less  degree  of  sensibility. 

Various  forms  of  instruments,  usually  called  hydrometers, 
have  been  proposed  for  ascertaining  the  specific  gravities  of 
substances,  and  more  particularly  of  liquids,  for  the  ordinary 
purposes  of  commerce.  The  indications  of  these  instruments  all 
depend  upon  the  fact,  that  a  body,  when  it  floats  in  a  liquid,  dis- 
places a  quantity  of  the  liquid  equal  to  its  own  weight.  Their 
accuracy  depends  upon  giving  them  such  a  shape,  that  the  part  of 
them  which  meets  the  surface  of  the  liquid  in  which  they  float 
is  a  narrow  stem,  of  which  even  a  considerable  length  displaces 
but  a  very  small  weight  of  the  liquid.  Thus  any  error  in  ob- 
serving the  degree  of  immersion  entails  upon  the  result  an 
effect  which  is  inconsiderable. 

The  principle  in  all  such  instruments  being,  in  the  main,  the 
same,  it  will  not  be  necessary  here  to  enter  into  further  details 
upon  them  than  to  describe  the  form  and  use  of  two  or  three  of 
the  most  remarkable. 

Sikes's  Hydrometer. 

This  instrument,  being  that  which  is  used  and  sanctioned  by 
law  for  the  collection  of  the  revenue  on  ardent  spirits,  &c.,  is 
entitled  to  particular  notice.  It  consists  of  a  brass  ball  G,  fig. 
61.,  the  diameter  of  which  is  one  inch  and  six  tenths.  Into  this 
ball,  at  C,  is  inserted  a  conical  stem  C  D,  about  one  inch  and 
an  eighth  long,  terminated  with  a  pear-shaped  bulb  at  D,  which 
is  loaded,  so  as  to  be  much  heavier,  bulk  for  bulk,  than  any 
other  part  of  the  instrument.  In  the  top  at  B  is  inserted  a  flat 
stem  B  A,  three  inches  and  four  tenths  in  length,  which  is  di- 
vided on  both  sides  into  eleven  equal  parts,  each  of  which  is 
subdivided  into  two.  This  instrument  is  accompanied  by  eight 
circular  weights,  such  as  W,  marked  with  the  numbers  10,  20, 


CHAP.  TIII.         NICHOLSON'S  HYDROMETER. 


121 


30,  40,  50,  60,  70,  and  80 ;  each  of  the  circu- 
lar weights  is  cut  as  represented  in  W,  so 
as  to  admit  the  thinner  part  of  the  conical 
stem  near  C  to  pass  to  the  centre  of  the 
weight ;  the  opening  is  wider  at  the  centre, 
so  as  to  allow  the  weight  to  slide  down  the 
stem  to  D,  where  the  thickness  prevents  its 
falling  off.  In  using  this  instrument  to  as- 
certain the  specific  gravity  of  spirits,  it  is  first 
plunged  in  the  liquid,  so  as  to  be  wetted  to 
the  highest  degree  on  the  scale :  it  is  then 
allowed  to  rise  and  to  settle  into  equilibrium. 
The  degree  upon  the  scale  at  the  surface  of 
the  liquid  indicates  the  quantity  immersed  ; 
and  by  the  assistance  of  tables  which  accom- 
pany the  instrument,  and  a  thermometer  by 
which  the  temperature  of  the  spirits  is  ob- 
served, the  specific  gravity  is  calculated  by 
rules  which  accompany  the  tables. 

Nicholson's  Hydrometer. 
This  instrument  is  susceptible  of  a  greater 
degree  of  accuracy  than  the  common  hydrom- 
eter observed  above,  and  a  corresponding 
degree  of  skill  and  attention  is  requisite  in 
the  use  of  it.    It  consists  of  a  hollow  ball  of 
brass  or  copper,  C  "D,fig.  62.,  to  which  a  small 
dish  A  B  is  attached  by  a  thin  steel  wire  Y 
the  diameter  of  which  does  not  exceed  the  fortieth  part  of  an 
inch.     A  stirrup  F  is  attached  to  the  lower  part  of  the  ball,  and 
carries  another  dish  E,  being  sufficiently  heavy  to  cause  the 
wire  Y  to  be  vertical  when  the  instrument  floats. 
The  weight  of  the  several  parts  of  the  instrument 
is  so  adjusted,  that  when  1000  grains  are  placed  in 
the  dish  A  B,  the  instrument  will  sink  to  a  point 
marked  about  the  middle  of  the  stem  in  distilled 
water,  at  the  temperature  of  60°.    Therefore  the 
weight  of  a  quantity  of  distilled  water,  equal  in 
volume  to  the  part  of  the  instrument  below  this 
point,  will  be  equal  to  the  weight  of  the  instrument, 
together  with  1000  grains.     To  find  the  specific 
gravity  of  any  other  fluid,  let  the  instrument  float 
upon  it,  and  let  the  weight  in  the  dish  A  B  be  so 
adjusted  that  the  instrument  will  be  immersed  as 
before  to  the  division  marked  upon  the  wire.     The 


Fig.  62. 


wei 
in 


**V*i**V*P    M*M*AW    U.|JVJi.l    H1C     TVJ1C*  _L  liC 

jight  of  the  instrument,  together  with  the  weight 
the  dish,  will  then  express  the  weight  of  the 


1255  A  TREATISE  ON  HYDROSTATICS.  CHAP.  VIII. 

liquid  which  the  instrument  displaces.  Thus  the  weight  of 
equal  bulks  of  the  liquid  and  distilled  water  at  the  temperature 
of  60°  will  be  ascertained,  and  thence  the  specific  gravity  of 
the  liquid  inferred. 

By  this  instrument  the  specific  gravities  of  solids  may  be  also 
ascertained.  Let  a  portion  of  the  solid  be  placed  in  the  dish 
A  B,  and  the  instrument  being  made  to  float  in  distilled  water 
at  60°,  let  additional  weights  be  thrown  into  the  dish  A  B  until 
the  instrument  sinks  to  the  mark  upon  the  wire.  The  weight 
of  the  solid,  together  with  these  additional  weights,  will  then, 
as  appears  from  what  was  stated  above,  amount  to  1000  grains ; 
therefore,  if  the  additional  weights  be  subtracted  from  1000 
grains,  the  remainder  will  be  the  exact  weight  of  the  solid.  Let 
the  solid  be  now  placed  in  the  lower  dish  E,  and,  as  before,  let 
weights  be  placed  in  the  dish  A  B,  until  the  instrument  again 
sinks  to  the  point  marked  on  the  stem  Y.  These  weights,  to- 
gether with  the  weight  immersed  in  the  water,  will  make  up 
1000  grains.  If,  therefore,  they  be  subtracted  from  1000  grains, 
the  remainder  will  be  the  weight  of  the  solid  in  water ;  having 
obtained  its  weight  in  air  and  in  water,  its  specific  gravity  may 
be  obtained  as  in  a  former  instance. 

The  wire  which  supports  the  dish  A  B  in  this  instrument  is 
so  thin,  that  an  inch  of  it  displaces  only  the  tenth  part  of  a  grain 
of  water.  The  accuracy  of  its  results  depending,  therefore,  on 
the  coincidence  of  the  mark  on  the  wire  Y  with  the  surface, 
which  can  always  be  ascertained  to  a  very  small  fraction  of  an 
inch,  will  come  within  the  limit  of  a  very  minute  fraction  of  a 
grain.  Specific  gravities  may  thus  be  obtained  correctly  to 
within  100,000th  part  of  their  whole  value,  or  to  five  places 
of  decimals. 

Fig'  Jg  De  Parcieux's  Hydrometer. 

This  instrument,  which  is  represented  in  Jig.  63., 
scarcely  differs  from  that  which  has  been  just  de- 
scribed. A  cup  C  is  connected  by  a  brass  wire  A  C, 
about  30  inches  long  and  a  12th  of  an  inch  in  diam- 
eter,  with  a  glass  phial  A  B,  which  is  loaded  with 
shot  at  the  bottom  to  keep  it  in  the  upright  position. 
The  length  of  the  wire  is  such,  that  the  phial,  when 
loaded  and  immersed  in  spring  water  at  a  medium 
temperature,  will  sink  to  a  point  about  an  inch  above 
A.  When  it  is  immersed  in  light  river  water,  it  will 
sink  to  about  20  inches  above  A.  The  specific 
gravities  of  different  kinds  of  water  are  compared 
by  this  instrument,  as  in  Nicholson's  hydrometer,  by 
throwing  weights  into  the  dish  C  until  the  instru- 
ment sinks  to  a  fixed  point  on  the  wire.  A  gradu- 
ated scale  H  E  is  attached  to  the  side  of  the  vessel 


CHAP,    Till.         DE    PARCIECX's    HYDROMETER.  123 

containing  the  »ater,  to  mark  the  degrees  of  immersion.  The 
sensibility  of  this  instrument  is  so  great,  that  a  pinch  of  any 
substance  soluble  in  water,  or  a  drop  of  any  liquid  which  mixes 
with  water,  being  combined  with  the  water  in  which  it  is  im- 
mersed, will  produce  an  observable  effect  upon  its  depth  of  im- 
mersion. 

This  instrument  was  invented  for  the  purpose  of  comparing 
the  specific  gravities  of  different  kinds  of  water. 

(96.)  The  power  of  determining  the  specific  gravity  of  bodies 
frequently  enables  us  to  declare  their  other  qualities,  and  some- 
times to  detect  their  component  parts,  if,  as  most  frequently 
happens,  they  are  formed  of  heterogeneous  materials.  Thu? 
spirits,  in  every  form  and  under  every  variety  in  which  they 
are  used  in  commerce  and  domestic  economy,  are  a  mixture  of 
alcohol  with  other  bodies,  of  which  water  is  the  principal.  As 
the  value  of  the  liquid  depends  upon  the  proportion  of  pure 
alcohol  which  it  contains,  it  becomes  a  problem  of  great  practi- 
cal importance  to  determine  this. 

In  like  manner  the  precious  metals,  whether  applied  to  use- 
ful or  ornamental  purposes,  are  generally  mixed  with  others  of 
-a  baser  species  in  a  greater  or  less  proportion.     These  cheaper 
elements  which  enter  into  the  composition  of  what  is  received 
for  gold  or  silver  are  called  alloys ;  and  it  is  obvious  that,  be- 
fore th>3  value  of  any  article  formed  of  such  a  material  can  be  s 
determined,  it  is  necessary  to  find  the  exact  proportion  of  alloy : 
which  itt  contains.  i 

Theso  considerations  suggest  a  class  of  problems  respecting 
the  specific  gravities  of  compound  bodies  and  their  constituent 
elements,  the  solution  of  which  is  of  great  practical  importance. 
This  solution,  however,  does  not  entirely  depend  on  mechani- 
cal principles,  as  we  shall  presently  explain  ;  and  even  so  far 
as  it  doe  B  depend  on  such  principles,  many  previous  conditions 
are  necessary  to  render  such  problems  determinate. 

If  two  bodies,  whose  specific  gravities  are  known,  be  mixed 
in  a  givon  proportion,  and  in  their  union  no  other  effect  be  pro- 
duced t)  lan  the  transfusion  of  the  particles  of  each  through  and 
among  those  of  the  other,  the  specific  gravity  of  the  compound 
is  a  matter  of  easy  computation.  The  general  principle  for  the 
solution  of  such  a  problem  will  be  collected  without  difficulty 
from  an  example. 

Example. — Let  gold  and  copper  be  united,  in  the  proportion 
of  20  measures  of  gold  to  3  of  copper.  The  specific  gravity  oi 
the  goltd  is  1925,  and  that  of  the  copper  890,  the  specific  gravity 
of  water  being  100.  Hence  the  calculation  may  be  made  as 
follow.')! ;  the  denomination  of  weight  used  being  immaterial, 
providing  it  be  tho  same  throughout  the  whole  investigation: — 


124  A  TREATISE  ON  HYDROSTATICS.        CHAP.  VIII. 

Weight  of  a  cubic  inch  of  water    .......     100 

Weight  of  a  cubic  inch  of  gold 1,925 

Weight  of  a  cubic  inch  of  copper  , 890 

Weight  of  20  cubic  inches  of  gold 38,500 

Weight  of?  cubic  inches  of  copper (5,230 

Weight  of  27  cubic  inches  of  the  compound    .     .    41,730 
Weight  of  one  cubic  inch  of  the  compound      .    .       l.,656f 

Hence  the  specific  gravity  of  the  compound  is  J,656f, 
that  of  water  being  100. 

If  the  proportion  of  the  ingredients  be  given  in  weight;,  as  so 
many  grains  of  gold  mixed  with  so  many  grains  of  copper,  the 
magnitudes  or  measures  of  these  weights  may  be  computed 
from  knowing  their  specific  gravities,  which  is  in  fact  the  weight 
of  a  given  magnitude.  The  preceding  method  of  calculation 
may  then  be  applied. 

If  more  than  two  bodies  be  united,  the  principle  on  whi-sh  the 
computation  is  conducted  will  be  the  same. 

In  the  example  just  given,  the  specific  gravity  of  th.e  com- 
pound was  the  object  of  inquiry,  the  specific  gravities  of  the 
components  being  supposed  to  be  given.  The  same  method 
of  calculation  would,  however,  discover  any  of  the  other  quan- 
tities which  enter  the  investigation  with  a  sufficient  nvjnber  of 
data.  Thus,  suppose  it  were  required  to  determine  one  of  the 
ingredients  of  a  compound  substance,  the  nature  and  quantity 
of  the  other  ingredient  being  known.  Let  the  specifi  c  gravity 
of  the  compound  be  determined  by  the  usual  means,  and  let  the 
quantity  of  the  given  ingredient  be  subtracted  from  the  whole 
quantity  of  the  compound,  and  the  remainder  will  be  the  quan- 
tity of  the  required  ingredient.  But  it  is  necessary  to  <  letermine 
its  specific  gravity. 

Example. — Let  the  compound  body  under  investigation  be 
supposed  to  be  composed  of  two  substances,  of  whiciS  gold  is 
one  ;  and  let  the  total  quantity  of  the  compound  be  27  cubic 
inches,  the  quantity  of  the  gold  being  20  cubic  inche  s.  Sup- 
pose that  we  ascertain  the  following  results  by  experii  nent : — 

Weight  of  27  cubic  inches  of  the  compound     .     .     44,730 

Weight  of  one  cubic  inch  of  gold 1,925 

Weight  of  20  cubic  inches  of  gold 58,500 

Weight  of  7  cubic  inches  of  the  alloy     ....      -6,230 
Weight  of  one  cubic  inch  of  the  alloy     ....          890 

Hence  the  specific  gravity  of  the  alloy  will  be  890 ;  a  nd  that 


CHAP.     VIII.          INGREDIENTS    OF    COMPOUNDS.  125 

being  'Known  to  be  the  specific  gravity  of  copper,  the  quality  of 
the  alloy  is  determined. 

When  tne  quality  of  the  alloy  is  known,  it  may  be  required 
to  determine  the  proportion  in  which  it  is  mixed  with  the  pre- 
cious metal.  In  this  case  the  specific  gravities  of  the  constitu- 
ent parts  are  supposed  to  be  given. 

Example.  —  Let  the  compound  be  one  of  gold  and  copper  as 
before,  the  specific  gravities  of  which  are  1925  and  890. 

Weight  of  a  cubic  inch  of  gold    .......     1,925 

Weight  of  a  cubic  inch  of  copper     ......        890 

Difference    ..............     1,035 

____  ____ 

Weight  of  a  cubic  inch  of  the  compound  by  experi- 
ment   ...........     ....     l,656f 

Wieight  of  a  cubic  inch  of  copper     ......        890 

Difference    ........     ......        76Gf 

As  the  former  difference  1035  is  to  the  latter  7(>6f  ,  so  is  1 
to  tlio  number  which  expresses  the  proportion  in  which  the 
metals  are  mixed.  Thus,  by  the  Rule  of  Three  :  —  1035  :  766$ 
:  :  1  :  766|  divided  by  1035,  or  which  is  the  same,  £-£.  Hence 
the  proportion  of  gold  contained  in  a  cubic  inch  of  the  com- 
pound is  20  parts  in  27,  and  there  are,  therefore,  7  parts  of  al- 
loy. The  demonstration  of  the  proportion  used  in  this  solution 
.scarcely  admits  of  a  sufficiently  elementary  explanation  to  be 
introduced  with  propriety  in  the  text.* 

If  the  object  be  to  detect  the*  exact  quantity  and  quality  of 
the  impure  or  heterogeneous  matter  contained  in  any  compound, 
it  will  not  be  sufficient  that  the  specific  gravity  of  the  compound 
and  that  of  the  principal  ingredient  bev  previously  known.  .  Thus, 
in  manufactured  gold,  it  is  not  enough  to  know  the  specific 
gravity  of  pure  gold,  and  that  of  the  alloyed  specimen  under 
investigation,  in  order  to  determine  the  quantity  and  quality  of 

*  Let  ^represent  the  proportion  of  gold,  and  i/  that  of  copper,  contained  in  ona 
cubic  inch  of  the  mixture.     Let  g  be  the  rpocirtc  gravity  of  the  gold,  c  that  of  the 
copper,  and  m  that  of  the  mixture.     The  weight  of  gold  contained  in  a  cubic  inch 
of  the  mature  is  xg,  and  tho  weight  of  coppor  ?/c,  and  the  weight  of  a  cubic  inch  of 
the  mixture  is  ?:i.    Hence  we  have 
x:r~\-yc—m 
-M-2,-1 


'••*=  - 

g—c 
or,  g  —  c  :  m  —  c   !  ;    1  :  x. 


That  i^  the  difference  between  the  npeciric  gravities  of  tho  gold  and  copper  is  to 
the  differe 
the  pr<por 


the  difference  between  the  specific  gravities  of  the  compound  and  copper,  as  1  is  to 
'  >rtion  of  gold  which  e^tj  in  a  i  ubic  inch. 


126 


A    TREATISE    ON    HYDROSTATICS.          CH.  IP.  VIII. 


the  alloy.  It  is  indispensably  necessary,  either  that  the  ;  specific 
gravity  of  the  foreign  matter  intermixed  with  the  pi  incipal 
ingredient  be  given,  or  that  some  data  may  be  furnisl  aed  by 
which  it  may  be  computed. 

Although  in  the  cases  of  alloyed  metals,  or  adulterated  1  .iquids, 
it  is  rarely  possible  to  detect  the  exact  quantity  and  qur  Jity  of 
foreign  matter  which  may  be  intermixed,  yet  we  may  ge  nerally 
pronounce  with  certainty  on  the  presence  of  some  adult, eration 
or  alloy.  The  specific  gravity  of  the  pure  substance;  being 
known,  if  that  of  the  specimen  under  inquiry  differ  fron  i  it,  the 
intermixture  of  foreign  matter  is  no  longer  doubtful'..  But 
what  that  heterogeneous  matter  is,  and  in  what  quantit/  it  is 
present,  is  a  problem  which  requires  the  aid  of  other  princi  pies. 
It  has  been  already  stated  that  spirits  of  every  kind  usod  in 
commerce,  are  mixtures  of  pure  alcohol  and  water  in  different 
proportions,  and  their  strength  depends  on  the  quantity  of  alco- 
hol which  is  mixed  with  a  given  quantity  of  water.  The  indi- 
cations of  the  hydrometer  immediately  betray  this. 

The  adulteration  of  milk  by  water  may  always  be  deti  ttted 
by  the  hydrometer,  and  in  this  respect  it  may  be  a  usefu  I  ap- 
pendage to  household  utensils.  Pure  milk  has  a  greater  sp(  jcific 
gravity  than  water,  being  103,  that  of  water  being  ICO.  A  very 
small  proportion  of  water  mixed  with  milk  will  produce  a  ^quid 
specifically  lighter  than  water. 

Although  the  hydrometer  is  seldom  applied  to  domestic  uses, 
yet  it  might  be  used  for  many  ordinary  purposes  which  oould 
scarcely  be  attained  by  any  other  means.  The  slightest  adul- 
teration of  spirits,  or  any  other  liquid  of  known  quality,  msy  be 
istantly  detected  by  it.  And  it  is  recommended  by 'its  cheap- 
ness, the  great  facility  of  its  manipulation,  and  the  simplicity  of 
its  results. 

(97.)  The  first  notion  of  using  the  buoyancy  of  solids  in  a 
liquid,  as  means  of  determining  the  nature  of  their  con  iponent 
parts,  is  attributed  to  Archimedes,  the  celebrated  mathen  latician 
and  natural  philosopher.  It  is  said  that  Hiero,  king  of  S}  -racuse, 
haying  engaged  an  artist  to  make  him  a  crown  of  gold,  wished 
to  know  whether  the  article  furnished  to  him  was  cor.  aposed, 
according  to  the  contract,  of  the  pure  and  unalloyed  met  al,  and 
yet  to  accomplish  this  without  defacing  or  injuring  the  crown, 
tie  referred  the  question  to  Archimedes.  The  philc  sopher 
while  meditating  on  the  solution  of  this  problem  happei  ling  to 
bathe,  his  attention  was  directed  to  the  buoyancy  of  his  1  >ody  in 
the  water,  and  thence  to  the  general  effect  produced  upc  >n  the 
apparent  weights  of  solids  by  their  immersion  in  liquids.  The 
whole  train  of  reasoning  which  has  been  followed  in  thi  J  pre- 
ceding chapters  instantly  flashed  across  his  mind.  He  pe  rceiv- 
ed  at  once  that  the  degree  of  buoyancy  or  the  weightiest  -  vould 


CHAP.  VIII.  TO    DETECT    ADULTERATION.  127 

betray  the  weight  of  the  metal  composing  the  crown,  compared, 
bulk  for  bulk,  with  pure  gold.  He  rushed  from  the  chamber  in 
a  transport  of  joy, ' exclaiming  aloud,  "Eureka!  Eureka!"  (/ 
have  found  it !  I  have  found  it .') 

If  the  tale  be  true,  the  joy  of  Archimedes  was  produced  not 
by  the  solution  of  the  particular  question  respecting  the  crown, 
but  by  perceiving  the  important  consequences  to  which  the  ex- 
tension of  the  principle  on  which  he  had  fallen  must  lead. 

(98.)  The  calculations  which  have  been  just  explained,  for 
ascertaining  the  specific  gravities  of  compound  bodies  when 
those  of  their  component  parts  are  known,  proceed  upon  the 
supposition  that  the  bulk  or  magnitudes  of  the  bodies  united  are 
not  altered  by  their  combination.  Thus,  if  ten  cubic  inches  of 
gold  be  alloyed  with  seven  cubic  inches  of  copper,  it  is  assum- 
ed that  the  mass  of  compound  metal  thus  obtained  will  measure 
17  cubic  inches.  In  like  manner,  if  a  pint  of  water  be  mixed 
with  a  pint  of  spirits,  the  computed  specific  gravity  of  the  mix- 
ture proceeds  upon  the  assumption  that  it  will  measure  a  quart. 
Experience  proves  this  supposition  to  be,  in  most  cases,  un- 
founded. When  the  constituent  atoms  of  two  bodies  are  trans- 
fused through  one  another  by  intimate  mixture,  it  is  found  that 
certain  properties  are  manifested  which  exhibit  a  reciprocal 
relation  between  them,  in  virtue  of  which  they  are  either  drawn 
together  into  closer  contact  and  compelled  to  occupy  a  less 
space,  or  are  mutually  repelled  and  made  to  occupy  a  greater 
space  by  attractive  or  repellent  forces,  which  are  called  into 
operation  by  the  contiguity  of  the  molecules  of  the  different 
bodies.  In  fact,  it  is  found  that  equal  measures  of  two  different 
Bodies,  being  combined  by  mixture,  will  produce  a  compound, 
the  measure  of  which  will  be  either  less  or 
Fig.  64.  greater  than  tvtfice  the  measure  of  either  of 
the  bodies  so  combined.  Thus,  a  cubic  inch 
of  gold  mixed  with  a  cubic  inch  of  copper 
will  produce  a  mass  of  metal  measuring  less 
than  two  cubic  inches.  It  follows,  therefore, 
that  the  component  particles  of  these  bodies 
have  been  forced  into  a  less  space  than  that 
which  they  occupied  separately  ;  and  there- 
fore, that  corresponding  affinities  or  attractive 
energies  have  been  awakened  by  their  com- 
bination. In  like  manner,  if  a  pint  of  pure 
water  and  a  pint  of  sulphuric  acid  be  mixed 
together,  the  compound  will  measure  less  than 
a  quart.  This  experiment  may  be  very  easily 
exhibited  in  the  following  manner  :— Let  A, 
Jig.  64.,  be  a  hollow  glass  ball,  having  a  neck 
at  the  top  B,  furnished  with  a  ground  glass  stopper  made  ex- 


128  A    TREATISE    OX    HYDROSTATICS.         CHAP.  VIII. 

actly  to  fit  it,  and  water  tight,  and  with  a  long  narrow  tube  C  D 
proceeding  from  the  bottom  and  closed  at  the  lower  end  D  ;  let 
this  vessel  be  filled  through  the  neck  B  with  sulphuric  acid  as 
far  as  the  top  of  the  tube  C  ;  then  let  water  be  carefully  poured 
in  till  the  ball  is  completely  filled  to  the  neck  ;  this  liquid,  being 
lighter  than  sulphuric  acid,  will  remain  in  the  ball  resting  on 
the  surface  of  the  sulphuric  acid  in  the  tube  below.  Let  the 
stopper  be  inserted  in  the  neck,  so  that  the  vessel  being  closed 
will  be  completely  filled  with  the  two  liquids :  holding  the  stop- 
per firmly  in  its  place,  let  the  vessel  be  now  inverted,  the  tube 
being  turned  upwards  and  the  stopper  downwards.  The  sul- 
phuric acid  will,  by  its  superior  weight,  fall  into  the  ball,  and 
the  water  will  rise  into  the  tube,  a  partial  mixture  taking  place 
by  reason  of  the  affinity  of  the  liquids :  this  inversion  being 
several  times  repeated,  the  liquids  will  at  length  be  perfectly 
mixed.  If  the  instrument  then  be  held  steadily  with  the  tube 
upwards,  it  will  be  four/d  that  the  liquids  no  longer  fill  it,  but 
that  several  inches  at  the  top  of  the  lube  will  be  empty.  Thus 
the  dimensions  of  the  liquids  will  be  considerably  contracted  by 
intermixture  ;  and  of  course  the  density  or  specific  gravity  will 
be  much  greater  than  if  the  liquids  were  mechanically  united 
without  any  diminution  of  their  volume. 

The  effect  here  described  will  be  found  to  be  attended  with 
another  very  remarkable  one.  The  liquids  at  the  commencement 
of  the  process  being  at  the  ordinary  temperature  of  the  atmos- 
phere, it  will  be  found  that  after  they  are  mixed  they  will 
acquire  so  great  a  degree  of  heat,  that  the  vessel  which  con- 
tains them  cannot  be  held  in  the  hand  without  pain.  This  ef- 
fect bears  a  close  relation  to  the  expansion  of  bodies  by  heat. 
If  the  communication  of  heat  to  a  body  causes  its  dimensions 
to  increase,  it  might  noturaliy  be  expected  that  any  cause 
which  would  produce  a  diminution  of  dimension  would  compel 
the  body  to  part  with  heat.  Thus  the  condensation  produced 
by  the  admixture  of  the  two  liquids  is  accompanied  by  the  evo- 
lution of  heat.  It  is  sufficient  barely  to  notice  this  effect  here, 
as  it  will  be  more  fully  explained  in  another  part  of  the  Cyclo- 
paedia. 

Although  the  method  of  completing  the  specific  gravity  of  a 
mixture,  "upon  the  supposition  that  its  constituent  elements 
suffer  no  change  of  dimension,  is  inapplicable  for  the  actual  de- 
termination of  the  specific  gravities  of  compounded  bodies,  yet 
such  computation  is  not  useless.*  The  only  exact  method  of 

*Let  c  and  c1  be  the  specific  gravities  of  the  component  parts,  and  m  the  specific 
gravity  of  the  mixture  ;  'let  a  and  a'  be  the  magnitudes  of  the  component  parts,  and 
a-f-a'  will  be  the  magnitude  of  tho  mixture.  The  weights  of  the  components  will 
be  a  c  and  a'  c',  and  the  weight  of  the  rr-ixturc  will  bo  a  c+a1  c',  which  is  the  sum 
of  the  weights  of  the  components  :  but  tlie  weight  of  the  mixture  will  r.leC  be  ex- 
pressed by  (rt-f-rr)  r,i ,-  hence 


CHAP.  VIII.          PENETRATION    OF   DIMENSIONS.  129 

ascertaining  the  degree  in  which  suhstances  contract  or  ex- 
pand their  dimensions  by  mixture  is  by  computing  the  specific 
gravity  which  the  mixture  would  have  were  such  change  of 
dimension  not  to  happen,  and  comparing  such  computed  spe- 
cific gravity  with  the  actual  specific  gravity  of  the  compound 
body  observed  by  experiment.  The  process  of  measurement 
is  not  susceptible  of  the  same  accuracy,  nor,  indeed,  of  any 
degree  of  accuracy  sufficient  for  scientific  purposes  :  were  it 
so,  however,  it  would  scarcely  be  so  simple  as  the  comparison 
of  the  computed  and  observed  specific  gravities.  The  quanti- 
ties of  the  two  substances  mixed  should  be  accurately  measur- 
ed before  mixture,  and  the  measure  of  the  compound  should  be 
afterwards  accurately  ascertained.  The  difference  between  the 
sum  of  the  measures  of  the  constituent  parts  and  the  measure 
of  the  whole  would  give  the  contraction  or  expansion  produced 
by  their  combination. 


ffl  C-fffl'  C' 

•••m=-THT  [ 

In  fact,  this  result  is  nothing  more  than  an  expression  denoting  that  the  specific 
gravity  of  the  compound  is  equal  to  its  weight,  divided  by  its  magnitude,  the  mag- 


nitude being  supposed  to  be  equal  to  the  sum  of  the  magnitudes  of  the  components 

In  some  cases,  the  weights  and  specific  gravities  of  the  components  are  given,  b 
not  their  magnitudes.    Let  w  and  to'  be  the  weights  ;  then  w=a  c,  and  w'=a'  c'. 


Therefore  a  =  —  and  o'  =  -  .    Hence 
c  c' 

tc_j_w'      tr-f-w' 


_  (»+»')  e  c' 

-  " 


I 
130  A    TREATISE    ON    HYDROSTATICS.  CHAP.    IX 


CHAP.  IX. 

HYDRAULICS 

TELOCITY  OF  EFFLUX  FROM  AN  APERTURE  IN  A  VESSEL, — PROPOR- 
TIONAL TO  THE  DEPTH  OF  THE  APERTURE,— EQUAL  TO  THE  VE- 
LOCITY ACQUIRED  IN  FALLING  THROUGH  THAT  DEPTH. — EFFECT 
OF  ATMOSPHERIC  RESISTANCE.— VENA  CONTRACTA. — RATE  AT 
WHICH  THE  LEVEL  OF  THE  WATER  IN  THE  VESSEL  FALLS. — 
LATERAL  COMMUNICATION  OF  MOTION  BY  A  LIQUID. — RIVER  FLOW- 
ING THROUGH  A  LAKE. — CURRENTS  AND  EDDIES.— EFFECTS  OF 
THE  SHAPE  OF  THE  BED  AND  BANKS  OF  A  RIVER.— FOBCE  OF  A 
LIQUID  STRIKING  A  SOLID,  OR  VICE  VERSA. — EFFECT  OF  AN  OAR. 
— WINGS  OF  A  BIRD. — DIRECTION  OF  THE  RESISTING  SURFACE. — 
EFFECT  OF  THE  VELOCITY  OF  THE  STRIKING  BODY. — SOLID  OF 
LEAST  RESISTANCE. — SHAPE  OF  FISHES  AND  BIRDS. — SPEED  OF 
BOATS  AND  SHIPS  LIMITED.— COMPARATIVE  ADVANTAGES  OF  RAIL- 
ROADS AND  CANALS. 

(99.)  WE  have  hitherto  confined  our  attention  chiefly  to 
those  effects  which  are  produced  by  the  pressure  transmitted 
by  liquids,  either  arising  from  their  own  weight  or  from  other 
forces  applied  to  them,  when  confined  within  certain  limits. 
When  any  of  the  limits  or  boundaries  which  confine  a  liquid 
are  removed,  the  force  which  before  was  expended  in  exciting 
pressure  on  such  boundary  or  limit,  will  now  put  the  liquid  in 
motion,  and  cause  it  to  escape  through  the  space  from  which 
the  opposing  limit  has  been  removed.  The  phenomena  exhib- 
ited under  such  circumstances,  form  the  subject  of  a  branch 
of  the  mechanical  theory  of  liquids  usually  called  hydraulics. 
It  embraces,  therefore,  the  effects  attending  liquids  issuing  from 
orifices  made  in  the  reservoirs  which  contain  them ;  water  forced 
by  pressure  in  any  direction  through  tubes  or  apertures,  so  as 
to  form  ornamental  jets ;  the  motion  of  liquids  through  pipes 
and  in  channels  ;  the  motion  of  rivers  and  canals  ;  and  the  re- 
sistance produced  by  the  mutual  impact  of  liquids  and  solids  in 
motion. 

It  is  the  peculiarity  of  this  branch  of  hydrostatics,  that,  from 
various  causes,  the  phenomena  actually  exhibited  in  nature  or 
in  the  processes  of  art  deviate  so  considerably  from  the  results 
of  theory,  that  the  latter  are  of  comparatively  little  use  to  the 
practical  engineer.  They  also  lose  a  great  part  of  their  charm 
for  the  general  reader,  from  the  impossibility  of  producing  from 
the  familiar  objects,  whether  of  nature  or  art,  examples  appo- 
sitely and'  strikingly  illustrative  of  the  general  truths  derived 
from  scientific  reasoning.  It  must  not,  however,  be  supposed 
that  the  results  of  such  investigations  are  false,  or  that  the  sci- 


CHAP.    IX.  HYDRAULICS.  131 

ence  itself,  or  the  instruments  by  which  it  proceeds,  are  defec- 
tive. The  difficulty  here  lies  rather  in  the  peculiar  nature  of 
the  phenomena,  and  the  number  of  disturbing  causes  which 
render  them  incapable  of  that  accurate  classification  and  gener- 
alization which  is  so  successfully  applied  in  almost  every  other 
department  of  physical  science. 

The  only  really  useful  method  of  treating  a  branch  of  knowl- 
edge so  circumstanced,  is  to  accompany  a  very  concise  account 
of  such  general  principles  as  are  least  inapplicable  to  practice, 
by  proportionately  copious  details  of  the  most  accurate  experi- 
ments which  have  been  instituted,  with  a  view  to  ascertain  the 
actual  circumstances  of  the  various  phenomena.  Such  details, 
however,  would  be  wholly  misplaced  in  the  present  treatise  ; 
we  shall,  therefore,  confine  ourselves  to  a  few  observations  on 
some  of  the  most  important  and  striking  phenomena  of  hydraul- 
ics ;  tracing  their  connection,  where  it  is  possible,  with  the 
various  analogous  effects  in  the  other  parts  of  the  mechanics 
of  solids  and  fluids. 

(100.)  If  a  small  hole  be  made  in  the  side  of  a  vessel  which 
is  filled  with  a  liquid,  the  liquid  will  issue  from  it  with  a  certain 
velocity.  The  force  which  thus  puts  the  liquid  in  motion  is 
that  which,  before  the  orifice  was  made,  exerted  a  pressure  on 
the  surface  of  the  matter  which  stopped  the  orifice.  It  is  obvi- 
ous, that  the  moving  force  of  the  water  which  thus  issues  from 
the  orifice  must  be  adequate  and  proportional  to  the  power 
which  produces  it.  But  this  power,  being  the  same  which  pro- 
duced the  pressure  upon  the  surface  of  the  vessel,  will  be 
proportional  to  the  depth  of  the  orifice  below  the  level  of  the 
liquid  in  the  vessel  (14.).  Hence  we  may  at  once  infer,  that 
water  will  issue  with  more  violence  from  an  orifice  at  a  greater 
depth  below  the  surface,  than  from  one  at  a  less  depth  ;  but  it 
still  remains  to  be  determined  what  the  exact  proportion  is  be- 
tween the  rapidity  of  efflux  and  the  depth  of  the  orifice. 

Let  A  B  C  D,  Jig.  65.,  be  a  vessel  with  perpendicular  sides, 
having  a  very  small  orifice  O  near  the  bottom.  Let  it  be  filled 
with  water  to  a  certain  height,  E  F,  above  O.  The  pressure 
corresponding  to  the  depth  O  E,  will  cause  the  water  to  flow 
from  O  with  a  certain  velocity.  Suppose  this  velocity  to  be  10 
feet  in  a  second  ;  and  suppose  that  by  this  means  a  gallon  of 
water  is  discharged  from  O  in  one  minute,  water  being  in  the 
mean  while  supplied  to  the  vessel  in  such  a  quantity  as  to 
maintain  the  level  of  the  water  in  the  vessel  at  E  F.  The  pres- 
sure at  O  being  therefore  always  the  same,  the  velocity  of  efflux 
will  be  uniform.  It  is  clear,  that  if  water  be  now  poured  into 
the  vessel,  so  as  to  fill  it  to  a  level  higher  than  E  F,  the  pres- 
sure at  O  being  increased,  the  velocity  of  efflux  at  O  will  be 
also  increased.  Let  it  be  required  to  determine  how  much 


132 


A    TREATISE    ON    HYDROSTATICS.  CHAP.    IX, 


Fig.  65. 


A 
E 


higher  than  E  F  it  will  be  necessary  to  fill  the  vessel,  in  order 
that  the  velocity  with  which  the  water  is  discharged  at  O  shall 
be  double  the  former  velocity.  The  momentum  or  moving  force 
communicated  to  the  water  discharged  from  the  orifice  in  one 
minute  would  in  this  case  be  four  times  that  which  was  com- 
municated to  it  in  the  former  case  ;  for,  since  the  rapidity  with 
which  the  water  is  discharged,  is  double  its  former  velocity, 
double  the  quantity  of  water  will  be  put  in  motion  in  one  minute  ; 
out  this  double  quantity  is  also  moved  with  a  double  speed ; 
hence  the  entire  moving  force  produced  in  a  minute  will  be  four 
times  the  moving  force  produced  in  the  former  case  in  the  same 
time.  If  the  same  quantity  of  water  only  had  been  put  in  mo- 
tion with  a  double  velocity,  the  moving  force  would  be  doubled ; 
but  the  quantity  of  water  moved  being  doubled  as  well  as  its 
speed,  the  moving  force  is  quadrupled.  Hence  it  follows,  that 
the  power  which  produces  this  effect  must  have  four  times  the 
energy  of  that  which  produced  the  effect  in  the  first  case  ;  but 
this  power  is  the  pressure  produced  at  the  orifice  O,  which  is 
proportional  to  the  depth  of  O  below  the  surface.  Hence  it 
follows  that  to  give  a  double  velocity  of  discharge  a  fourfold 
depth  is  necessary.  If  the  vessel  A  B  C  D  be  filled  to  the 
level  E'  F',  so  that  E'  O  shall  be  four  times  E  O,  then  the  veloci- 
ty of  discharge  at  O  will  be  double  the  velocity  when  the  level 
was  at  E  F. 

By  similar  reasoning  it  may  be  concluded  that,  to  obtain  a 
threefold  velocity,  a  ninefold  depth  is  necessary;  for  a  fourfold 
velocity,  sixteen  times  the  depth  will  be  required,  and  so  on : 
in  fact,  in  whatever  proportion  the  velocity  of  efHux  is  increas- 
ed, the  quantity  of  liquid  discharged  in  a  given  time  must  be 
also  increased ;  and,  therefore,  the  pressure  or  the  depth  must 
not  only  be  increased  in  proportion  to  the  velocity,  but  also  as 
many  times  more  in  proportion  to  the  quantity  discharged. 
Thus  the  depth  of  the  orifice,  below  the  surface,  will  always  be 


CHAP.    IX. 


TELOCITY    OF    EFFLUX. 


133 


in  proportion  to  what,  in  mathematics,  is  called  the  square  of 
the  velocity  of  discharge. 

If  in  a  vessel  A  B  C  D,  Jig.  66.,  filled  with  a  liquid,  a  small 


Fig.  66. 


to 


-  ///' 

O 


hole,  O,  be  made  at  one  inch  below  the  surface  E  F  ;  and  an- 
other, O7,  at  4  inches  below  it ;  a  third,  O",  at  9  inches ;  a 
fourth,  O"',  at  sixteen  inches  ;  and  a  fifth,  O"",  at  25  inches  ; 
the  velocities  of  discharge  at  these  several  holes  will  be  in  the 
proportion  of  1,  2,  3,  4,  and  5.  If  the  upper  line  in  the  follow- 
ing table  express  the  several  velocities  of  discharge,  the  lower 
one  will  express  the  corresponding  depths  of  the  orifices  : — 


Velocity. 

1 

1 

2 
4 

3 

9 

4 

le" 

5 

25~ 

6 
36 

7 
49 

8 

9 
81 

10 

100 

Depth. 

64 

It  is  impossible  to  contemplate  the  relation  exhibited  in  this 
table  without  being  struck  by  the  remarkable  coincidence 
which  it  exhibits  with  the  relation  between  the  height  from 
which  a  body  falls  and  the  velocity  acquired  at  the  end  of  the 
fall.*  To  produce  a  two  fold  velocity,  a  four  fold  height  is  neces- 
sary. To  produce  a  threefold  velocity,  a  ninefold  height  is  re- 
quired. For  a  fourfold  velocity,  a  sixteenfold  height  is  required ; 
and  30  on.  Thus  it  appears,  that  if  a  body  were  allowed  to  fall 
from  the  surface  F  of  the  water  in  the  vessel  downwards  to- 
wards C,  and  unobstructed  by  the  fluid,  it  would,  on  arriving  at 


12 


*  Cab.  Cyc.  Mechanics,  p.  66. 


134  A    TREATISE    OX    HYDROSTATICS.          CHAP.    IX. 

each  of  the  orifices  above  described,  have  velocities  proportional 
to  those  of  the  water  discharged  at  the  orifices  respectively. 
Thus,  whatever  velocity  it  would  have  acquired  on  arriving  at 
O,  the  first  orifice,  it  would  have  double  that  velocity  on  arriv- 
ing at  O,  the  second  orifice,  three  times  that  velocity  on  arriving 
at  the  third,  O",  and  so  on.  Now,  it  is  evident  that  if  the  velo- 
city of  efflux  at  any  one  of  the  orifices  be  equal  to  the  velocity 
acquired  by  the  body  in  falling  from  the  surface  F  to  that 
orifice,  then  the  velocities  acquired  at  each  of  the  orifices  will 
be  equal  to  the  velocities  of  discharge  respectively.  Thus,  if 
the  velocity  acquired  in  falling  from  F  to  O  be  equal  to  the  ve- 
locity of  discharge  at  O,  then  the  velocity  acquired  in  falling 
from  F  to  O'  being  double  the  former,  will  be  equal  to  the 
velocity  of  discharge  at  O' ;  and  in  like  manner  the  velocity  ac- 
quired at  O"  being  three  times  the  velocity  at  O,  will  be  equal 
to  the  velocity  of  discharge  at  O".  In  order,  therefore,  to  es- 
tablish the  remarkable  fact  that  the  velocity  with  which  a  liquid 
spouts  from  an  orifice  in  a  vessel,  is  equal  to  the  velocity  which 
a  body  would  acquire  in  falling  unobstructed  from  the  surface 
of  the  liquid  to  the  depth  of  the  orifice,  it  is  only  necessary  to 
prove  the  truth  of  this  principle  in  any  one  particular  case. 
Now  it  is  manifestly  true,  if  the  orifice  be  presented  down- 
wards, and  the  column  of  fluid  over  it  be  of  very  small  height ; 
for  then  this  indefinitely  small  cdlumn  will  drop  out  of  the  ori- 
fice by  the  mere  effect  of  its  own  weight,  and  therefore  with 
the  same  velocity  as  any  other  falling  body  ;  but  as  fluids  trans- 
mit pressure  equally  in  all  directions,  the  same  effect  will  be 
produced  whatever  be  the  direction  of  the  orifice.  Hence  it  is 
plain  that  the  principle  just  expressed  is  true  when  the  depth 
of  the  orifice  below  the  surface  is  indefinitely  small ;  and  since 
it  is  true  in  this  case,  it  must,  according  to  what  has  been  al- 
ready explained,  be  also  true  in  every  other. 

(101.)  From  this  theorem  it  follows,  as  a  necessary  conse- 
quence, that  if  the  orifices  from  which  the  liquid  is  discharged 
be  presented  upwards,  the  jets  of  liquid  which  would  escape 
from  them  would  rise  to  a  height  equal  to  the  level  of  the  liquid 
in  the  vessel.  Thus,  in  Jig.  67.,  if  E  F  be  the  surface  of  the 
liquid,  and  O,  O',  O".  O'",  be  four  orifices  at  different  depths, 
all  opening  directly  upwards,  the  liquid  will  spout  from  each  of 
them  with  the  velocity  which  a  body  would  acquire  in  falling 
from  the  level  of  the  surface  E  F  G  to  the  orifices  respectively, 
and  consequently  the  liquid  must  rise  to  the  same  height  before 
it  loses  the  velocity  with  which  it  was  discharged.  Hence 
the  jets  severally  issuing  from  the  orifices  will  rise  to  the 
height  F  G. 

(102.)  These  important  theorems  must,  however,  be  submit- 
ted to  considerable  modifications  before  they  can  be  considered 


CHAP.    IX. 


CONTRACTED    VEIN. 


135 


FiS.  67. 


D 


as  applicable  in  practice.  In  the  preceding  investigation,  we 
have  considered  the  orifice  to  be  indefinitely  small,  so  that 
every  point  of  it  may  be  regarded  as  at  the  same  depth  below 
the  surface  ;  we  have  also  considered  that  the  fluid  in  escaping 
from  the  orifice  is  subject  to  no  resistance  from  friction  or  other 
causes  ;  and  also  that  in  its  ascent  in  jets  it  is  free  from  atmos- 
pheric resistance.  In  practice,  however,  all  these  causes  pro- 
duce very  sensible  effects  ;  and  the  consequence  is,  that  the 
actual  phenomena  vary  very  considerably  from  the  results  of 
theory.  The  velocity  of  efflux  is,  from  the  moment  the  orifice 
is  opened,  diminished  by  the  friction  of  the  liquid  against  the 
sides  of  the  pipe  or  opening  through  which  it  passes.  After  it 
escapes,  the  resistance  of  the  air  produces  a  sensible  effect 
upon  the  movement  of  the  fluid  particles.  This  resistance  in- 
creases even  more  rapidly  than  the  velocity,  so  that  the  jets 
which  escape  from  the  lower  orifices  are  still  more  resisted  in 
proportion  than  those  from  the  higher,  and  consequently  they 
do  not  rise  even  near  the  level  of  the  fluid  in  the  vessel. 

As  the  liquid  is  gradually  discharged  from  the  orifice,  the 
mtents  of  the  vessel  descend,  the  various  particles  falling  in 
..nes  nearly  perpendicular;  but  when  they  approach  near  the 
orifice  from  which  they  are  to  escape,  they  begin  to  change 
their  direction,  and  to  tend  toward  the  orifice,  so  that  their  mo- 
tion is  in  lines,  converging  towards  the  opening,  and  meeting 
at  a  point  outside  it.  These  effects  will  be  produced  whether 
the  opening  be  in  the  bottom  or  in  the  side  of  the  vessel.  They 


136 


A    TREATISE    ON    HYDROSTATICS. 


CHAP.    IX. 


Fig.  68. 


may  be  rendered  visible  by  using  a  glass  vessel  filled  with 
water,  in  which  filings  or  small  fragments  of  solid  substances 
are  suspended,  and  which  are  carried  along  by  the  motion  of 
the  currents. 

If  a  vessel  be  allowed  to  empty  itself  by  an  orifice  in  the 
bottom,  the  surface  of  the  liquid  will  gradually  descend,  main- 
taining its  horizontal  position;  but,  when  it  comes  within  a 
small  distance,  about  half  an  inch,  of  the  bottom,  a  slight  de- 
pression or  hollow  will  be  observed  in  that  part  of  the  surface 
which  is  immediately  over  the  orifice.  This  will  increase  until 
it  assume  the  shape"  of  a  cone  or  funnel,  the  centre  or  lowest 
point  of  which  will  be  in  the  orifice,  and  the  liquid  will  be  ob- 
served flowing  in  lines  directed  to  this  centre.  This  effect 
will  be  better  understood  by  referring  to  jig. 
68.,  where  the  direction  of  the  currents  and 
the  contracted  vein  are  exhibited. 

As  the  particles  of  liquid  in  approaching 
the  orifice  move  in  directions  converging  to 
a  point  outside  it,  it  is  plain  that  the  column 
of  fluid  which  escapes  from  the  vessel  will 
be  narrower  or  more  contracted  at  the  point 
towards  which  the  motion  of  the  liquid  con- 
verges  than  it  is  either  before  it  arrives  at 
that  point  or  after  it  has  passed  it.  This 
contraction  of  the  jet  produced  by  the  pe- 
culiar directions  which  the  motions  of  the 
fluid  particles  take,  was  first  noticed  by  New- 
ton, who  gave  it  the  name  of  the  vena  con- 
tracta  or  the  contracted  vein  of  fluid.  The 
distance  from  the  orifice  at  which  the  great- 
est contraction  of  the  jet  takes  place  depends, 
with  certain  limitations,  on  the  magnitude  of 
the  orifice.  If  the  orifice  be  circular  and 
small,  its  distance  is  equal  to  half  the  diame- 
ter of  the  orifice,  and  the  magnitude  of  the 
jet  at  its  most  contracted  point  bears  to  the 
magnitude  of  the  orifice,  according  to  New- 
ton, the  proportion  of  1000  to  1414,  and  ac- 
cording to,  Bossut,  the  proportion  of  1000  to 
1600. 

It  will  be  evident,  upon  very  slight  consideration,  that  if  the 
liquid  be  suffered  to  escape  by  a  cylindrical  tube,  the  contrac- 
tion of  the  vein  will  be  greatly  diminished.  In  this  case  the 
proportion  of  the  magnitude  of  the  most  contracted  part  to 
that  of  the  bore  of  the  tube  is  1000  to  1200. 

As  the  same  quantity  of  fluid  which  passes  in  any  given  time 
through  the  orifice  must  pass  in  the  same  time  through  the 


CHAP.  IX.  RATE  OF  EFFLUX.  137 

narrower  space  of  the  contracted  vein,  it  follows  that  it  must 
pass  through  this  place  with  a  proportionally  greater  velocity. 
Its  velocity,  therefore,  at  the  point  called  the  contracted  vein, 
is  greater  than  at  the  orifice  in  the  proportion  1414  to  1000, 
according  to  Newton's  calculation. 

In  applying  the  theorem  which  has  been  established  respect- 
ing the  equality  of  the  velocity  of  the  efflux  to  that  of  a  body 
which  has  fallen  from  the  surface  to  the  orifice,  it  is  the  veloci- 
ty of  the  contracted  vein  which  should  be  regarded,  that  being 
the  point  at  which  the  pressure  produces  its  greatest  effects. 

(103.)  In  the  preceding  investigation  we  have  supposed 
liquid  to  be  supplied  to  the  vessel  as  fast  as  it  is  discharged,  so 
that  the  surface  is  maintained  at  the  same  height  above  the 
orifice.  The  pressure  is  therefore  constant,  and  the  velocity 
of  efflux  uniform.  But  if  a  vessel  discharge  its  contents  by  an 
orifice  in  the  lower  part,  then  the  surface  will  continually  de- 
scend. The  pressure  at  the  orifice  will  be  continually  dimin- 
ished, and  the  square  of  the  velocity  of  discharge,  which  is 
proportional  to  this  pressure,  will  suifer  a  corresponding  dimi- 
nution. Hence  it  appears  that  the  velocity  of  discharge  is 
continually  less  until  the  surface  falls  to  the  level  of  the  orifice. 

It  is  not  difficult  to  perceive,  that  an  invariable  proportion 
must  subsist  between  the  velocity  of  discharge  and  the  velocity 
with  which  the  surface  of  the  liquid  in  the  vessel  falls.  Sup- 
pose that  the  magnitude  of  the  orifice  is  the  hundredth  part  of 
the  magnitude  of  the  surface  of  the  liquid,  and  that  the  rate  of 
discharge  at  any  moment  is  such  that  a  cubic  inch  of  the  liquid 
would  be  discharged  in  one  second  :  in  that  time  a  column  of 
the  liquid  will  pass  through  the  orifice,  whose  base  is  equal  to 
the  orifice,  and  whose  height  is  such  that  its  entire  magnitude 
will  be  a  cubic  inch.  In  the  same  time  the  level  of  the  liquid 
in  the  vessel  will  fall  through  a  space  which  would  require  a 
cubic  inch  of  the  liquid  to  fill.  This  space  will  be  just  as  much 
less  than  the  height  of  the  former  column,  as  the  magnitude  of 
the  orifice  is  less  than  the  magnitude  of  the  surface  of  the 
liquid  ;  that  is,  in  the  instance  assumed,  the  space  through 
which  the  surface  will  descend  in  one  second  will  be  the  hun- 
dredth part  of  the  space  through  which  the  liquid  projected  from 
the  orifice  would  move  in  a  second,  if  its  velocity  were  contin- 
ued uniform. 

By  the  same  reasoning,  it  may  be  inferred  generally,  that  the 
velocity  with  which  the  surface  descends  bears  to  the  velocity 
of  discharge  the  same  ratio  as  the  magnitude  of  the  orifice 
bears  to  the  magnitude  of  the  surface. 

Since  it  has  been  already  proved  that  the  square  of  the  velo- 
city of  discharge  is  proportional  to  the  depth  of  the  orifice,  it 
follows,  from  what  has  been  just  stated,  that  the  square  of  the 


138  A    TREATISE    ON    HYDROSTATICS.  CHAP.    IX. 

velocity  with  which  the  surface  descends  is  also  proportional 
to  the  depth  of  the  orifice.  It  is  proved  in  mechanics,  that 
when  a  body  is  projected  upwards,  commencing  with  a  certain 
velocity,  the  square  of  its  velocity  diminishes  in  proportion  t 
its  distance  from  its  point  of  greatest  elevation.  It  therefor>. 
follows,  that  such  a  body  is  retarded  as  it  approaches  its  great- 
est height,  according  to  the  same  law  as  the  velocity  of  the 
surface  of  a  liquid  in  descending  is  retarded  as  it  approaches 
the  orifice  at  which  it  is  discharged. 

Thus  all  the  properties  established  in  mechanics  respecting 
bodies  projected  upwards  and  retarded  by  the  force  of  gravity, 
may  be  applied  to  the  descent  of  the  surface  of  a  vessel  which 
is  emptied  by  an  aperture  in  any  part  below  that  surface.  The 
initial  velocity  of  the  surface  is  easily  found.  The  velocity  of 
efflux  at  the  orifice  is  that  which  would  be  acquired  by  a  body 
falling  from  the  surface  to  the  orifice,  and  may  be  determined 
by  the  ordinary  principles  of  mechanics.*  This  velocity,  being 
diminished  in  the  proportion  of  the  magnitude  of  the  surface  of 
the  liquid  to  the  magnitude  of  the  orifice,  will  give  the  initial 
velocity  of  the  surface  in  its  descent.  The  velocity  at  any 
other  elevation  may  be  calculated  upon  the  principle  that  the 
squares  of  the  velocities  at  any  two  elevations  above  the  ori- 
fice are  proportional  to  these  elevations. 

It  is  proved  in  mechanics,  that  if  a  body  be  projected  up- 
wards with  a  certain  velocity,  the  height  to  which  it  will  rise 
will  be  equal  to  half  the  space  through  which  it  would  move  in 
the  same  time  with  the  velocity  of  projection  continued  uni- 
form. Hence,  by  analogy,  we  infer,  that  the  time  which  the 
surface  of  a  liquid  takes  to  fall  from  any  given  elevation  to  the 
orifice,  is  equal  to  the  time  it  would  take  to  move  through  twice 
that  elevation  with  the  initial  velocity  continued  uniform.  NOAV 
as  this  initial  velocity  is  known,  the  time  which  the  surface 
would  take  to  move  through  twice  the  elevation  with  it  may  bo 
computed ;  and,  therefore,  the  time  which  the  surface  takes  to 
move  from  any  given  elevation  to  the  orifice  will  be  obtained. 

Hence  it  is  "easy  to  infer,  that  the  time  in  which  a  vessel  will 
empty  itself  through  a  hole  in  the  bottom  is  equal  to  the  time  it 
would  take  to  discharge  twice  the  quantity  of  fluid  contained  in 
the  vessel,  if  the  initial  velocity  were  continued  uniform. 

(104.)  If  a  stream  of  liquid  be  impelled  through  a  reservoir, 
in  which  the  liquid  is  at  rest,  it  is  evident  that  it  will  drive  be- 
fore it  those  parts  of  the  liquid  which  impede  its  course  ;  but, 
independently  of  this,  it  will  produce  other  motions  in  those 
parts  of  the  liquid  in  the  reservoir  neer  which  it  passes.  Let 
us  suppose  a  river  to  enter  an  extended  lake  at  one  extremity, 

*  Cab.  Cyc.  Mechanics,  chnp.  vii. 


CHAP.  IX. 


LATERAL    MOTION. 


and  to  issue  from  it  at  the  other ;  the  bed  of  the  river  being 
more  shallow  and  contracted  than  the  lake.  If  a  hollow  chan- 
nel or  aqueduct  were  formed  across  the  lake,  equal  in  magni- 
tude and  shape  with  the  bed  of  the  river,  the  water  of  the  river 
would  flow  across  the  lake  without  producing  any  effect  upon 
the  waters  of  the  lake,  being  separated  from  them  by  the  chan- 
nel or  aqueduct  which  we  have  supposed.  If  the  surface  of  the 
river,  flowing  in  the  channel,  coincide  with  the  level  of  the  sur- 
face of  the  lake,  the  channel  or  aqueduct  will  sustain  no  pres- 
sure or  strain,  or,  more  properly,  the  pressures  which  it  will 
suffer  on  all  sides  will  be  equal ;  the  waters  of  the  lake  press- 
ing it  upwards  and  inwards,  with  forces  exactly  equal  to  those 
by  which  the  waters  of  the  river  press  it  downwards  and  out- 
wards. It  is  clear,  therefore,  that  the  channel  has  no  effect  in 
sustaining  or  neutralizing  any  hydrostatical  pressure,  and  that 
its  removal  will  not  call  into  action  any  force  of  this  kind. 
Suppose  it  then  removed,  and  the  waters  of  the  lake  themselves 
to  form  the  channel  through  which  the  waters  of  the  river  flow. 
Shall  we  conclude,  that  in  this  case  the  waters  of  the  river  will 
continue  to  flow  through  those  of  the  lake,  the  latter  remaining 
quiescent,  and  the  two  masses  of  liquid  being  unmingled  ?  It 
has  been  found  by  experiment  that  such  will  not  be  the  effect. 
The  current  of  the  fiver  flowing  in  contact  with  the  waters  of 
the  lake  will  impart  to  them  a  share  of  its  own  motion ;  and 
these  again  will  communicate  the  motion  to  those  beyond  them, 
until  at  length  the  waters  of  the  lake,  to  a  great  extent,  on  each 
side  of  the  course  of  the  river,  are  put  in  motion. 

The  following  experiment  was  instituted  by  Venturi  to  illus- 
trate the  principle  of  the  lateral  propagation  of  motion  by  a 
liquid.  A  horizontal  pipe  A  B,  jig.  69.,  was  introduced  into  a 

Fig.  69. 


vessel  C  D  E  F,  which  was  previously  filled  with  water  to  the 
level  G  H.  Opposite  to  the  mouth  of  A  B,  and  at  a  short  dis- 
tance from  it,  was  placed  a  small  rectangular  canal  K  L  M  N  of 


A    TREATISE    ON    HYDROSTATICS.  CHAP. 


thin  metal,  with  a  curved  bottom,  perpendicular  sides,  and  open 
at  the  top.  This  canal  was  so  placed  as  to  be  capable  of  con- 
ducting  a  stream,  flowing  in  at  N  K,  over  the  edge  of  the  vessel 
F  and  discharging  it  at  M  L.  The  pipe  A  B  communicates 
with  a  reservoir  R,  kept  constantly  filled  to  the^ame  height,  so 
that  the  water  issues  from  B  continually,  with  the  same  rapidity 
Ihe  current  flowing  from  B  passes  through  the  water  in  the 
reservoir  C  D  E  F  in  the  space  between  B  and  K,  and  enters 
the  curved  canal  K  L  :  it  is  forced  up  this  by  the  velocity  with 
which  it  issues  from  B,  and  flows  out  at  L.  By  this  arranffe- 
|nt  a  current,  equal  in  magnitude  to  the  pipe  A  B,  is  contin- 
ually flowing  through  the  water  in  the  reservoir  C  D  E  F  in 
the  space  between  B  and  N  K. 


n  ,i     r  been  found  by  exPermient  to  be,  that 

the  who  e  of  the  liquid  m  the  vessel  C  D  E  F,  which  is  above 
the  level  B  K  is  carried  with  the  liquid  which  passes  from  the 
tube  A  B  up  the  canal  K  L,  and  discharged  at  L.  The  surface 
G  H  gradually  falls,  and  is  soon  reduced  to  the  level  B  K,  where 
it  remains. 

The  lateral  communication  of  motion  by  fluids,  here  describ- 
ed is  not  confined  to  the  case  where  the  fluid  to  which  the 

•toon  is  imparted  is  of  the  same  kind  as  that  from  which  the 
motion  ls  received.  A  current  of  water  passing  through  the 
21*5  g  V£  t0  he  ^mediately  contiguous  to  it  a  motion  in 
™  Same/I;rect;on-  jf  a  feather,  or  any  other  light  body,  be 
ovefthe'sn  f7  fn§r  fine,si]ken  thread>  and  ^Id  immediately 

e  °  aapid 


i     i    a/api  sream'  ut  not  in  c°ntact  *ith  it, 

be  found  to  be  driven  along  in  the  direction  of  the  stream 

bksnfSame  nThner  iS  U  W°Uld  happen  Were  *  exposed  to  a 
blast  of  air.     this  effect,  as  might  naturally  be  expected,  is 

greatly  increased  when  the  velocity  of  the  stream  is  very  con! 
mderable.  A  cascade,  which  falls  from  a  great  elevation,  pro- 
duces a  current  of  air,  the  force  of  which  can  scarcely  be  whh- 
tood  Venturi,  who  investigated  and  explained  this  phenome- 
non, observed  a  remarkable  example  of  it,  in  a  waterfall,  which 

R°Che  Mel0*>  °n  ^  «*i  ^  La 


'  1°'  rePJ?seJt  the  surface  of-  a  river,  N  R  and  O  S 
K  Spe     /i3  b^lks  ;  SUppose  the  current  to  run  in  ^e 

of  theb     IT    '  °?  -1Ct  5  A  be  an  dbstade  Pr°Jecting  ^om  one 
the  banks  and  impeding  its  course  :  the  water  will  thus  be 

e°e 


theDeomt°re^g  Gr  ab°Vf  B  A'  and  t0  discha^e  itself  round 
the  point  A  with  increased  velocity.    The  liquid  in  the  space 


CHAP.  IX.  EDDIES    OF    RIVERS.  141 


B  D  C  A  being  protected  from  the  force  of  the  descending 
stream  by  the  obstacle  B  A,  will  at  first  be  quiescent ;  but  the 
rapid  flow  of  the  water  from  the  point  A  will  communicate  mo- 
tion to  the  lateral  particles  in  the  space  C,  and  will  convey  them 
forward.  The  particles  at  E  will  then  become  slightly  depress- 
ed, and  the  remoter  particles  towards  D  will  have  a  tendency 
to  fill  the  depression ;  the  current  from  A  to  C  will,  however, 
continue  to  carry  them  off,  and  a  hollow  will  continue  in  the 
centre  of  the  space  A  C  D.  The  water  between  A  and  C  is 
thus  acted  upon  by  two  forces  ;  viz.  the  force  communicated  to 
it  laterally,  and  tending  to  carry  it  down  the  stream  in  the 
direction  A  C,  and  the  tendency  which  it  has  by  its  gravity  to 
fill  toAvards  the  centre  of  the  cavity  E.  These  two  forces  are 
precisely  analogous  to  those  by  which  a  body  is  caused  to  move 
in  a  circular  orbit,  viz.  a  projectile  force  at  right  angles  to  the 
radius  of  the  circle,  and  an  attractive  force  continually  solicit- 
ing the  body  to  the  centre.  The  water  by  this  means  is  whirled 
round  in  an  eddy,  which  is  continually  maintained  by  the  acr 
tion  of  the  stream  in  rushing  from  the  point  A. 
•  A  sudden  contraction  of  the  bed  of  the  river,  followed  imme- 
diately by  a  widening  of  the  banks,  as  at  N  O  P  Q,  will  produce 
'he  same  effect  as  two  obstacles,  such  as  B  A,  placed  on  oppo- 
site sides  of  the  river  ;  consequently,  under  such  circumstances, 
eddies  will  be  observed  on  both  sides  at  P  and  Q,  immediately 
after  passing  the  contraction. 

The  stream  of  water  shooting  from  A  will  strike  the  opposite 
bank  at  G  H,  and  will  be  reflected  from  it  in  the  direction  H  S ; 
the  effect  will,  therefore,  be  the  same  at  H  as  if  the  current 
encountered  an  obstacle  there  similar  to  B  A,  and,  consequent- 
ly, eddies  will  be  repeated  in  the  space  near  R.  It  follows, 
therefore,  that  a  sudden  contraction  of  the  banks,  succeeded  by 
a  widening,  will  not  only  produce  eddies  immediately  adjacent 
to  the  contraction,  but  that  these  eddies  will  be  continued  for  a 
certain  space  afterwards. 

Similar  effects  may  be  expected  by  inequalities  in  the  bottom 
of  a  river ;  but,  instead  of  taking  place  as  just  described,  in  a 
direction  parallel  to  the  surface,  they  will  be  produced  in  a  plane 


142  A  TREATISE    O.\    HYDROSTATICS.  CHAP.  IX. 

perpendicular  to  it,  and  the  eddies  will  be  presented  upwards 
like  the  curling  on  the  crest  of  a  wave. 

Let  Jig.  71.  represent  the  section  of  a  river  perpendicular  to 


Ti' 


its  surface,  A  K  exhibiting  the  shape  of  the  bottom.  In  the 
case  of  a  gentle  slope,  such  as  ABC,  let  us  first  suppose  the 
space  A  B  C  to  be  filled  with  water,  which  is  quiescent,  the 
stream  of  the  river  running  upon  its  surface  A  C  ;  the  motion 
of  the  river  will  be  gradually  communicated  to  the  water  below 
A  C,  so  as  to  give  it  a  motion  from  A  towards  C.  The  shape 
of  the  bottom  ABC  will  cause  it  to  be  projected  from  C  to- 
wards the  surface,  forming  a  vertical  eddy  which  will  frequently 
terminate  in  a  curling  wave.  In  this  case  B  C  acts  in  the  same 
manner  upwards  as  B  A,  in  Jig.  70.,  did  laterally.  If  the  ex- 
tremities of  the  hollow  be  abrupt,  as  at  D  G,  subaqueous  eddies 
will  be  produced. 

All  these  effects  may  be  exhibited  experimentally,  by  causing 
water  to  flow  through  artificial  channels  with  glass  sides. 

It  will  be  evident  from  all  that  has  been  stated,  that  irregu- 
larities in  the  bottom  and  sides  of  rivers  must  necessarily  retard 
their  currents ;  the  force  which  would  otherwise  carry  the 
stream  directly  down  its  channel  is  here  wasted  in  producing 
lateral  and  oblique  motions.  All  the  moving  force  of  the  water 
in  an  eddy  must  be  originally  derived  from  the  precipitous  de- 
scent of  the  stream,  which  is  therefore  robbed  of  all  the  power 
requisite  for  the  maintenance  of  such  effects.  We,  therefore, 
perceive  why  the  velocity  of  rivers,  in  their  descent  to  the  ocean, 
is  always  much  less  than  that  which  would  be  calculated  upon 
mechanical  principles,  supposing  them  to  flow  in  a  perfectly 
even  and  regular  channel.  In  fact,  the  effects  of  such  inequal- 
ities partake,  in  a  certain  degree,  of  the  nature  of  friction ;  they 
are,  as  it  were,  friction  on  a  large  scale.  It  is  also  evident  why 
rivers,  the  beds  of  which  descend  towards  the  sea  with  equal 
acclivities,  yet  may  have  very  different  velocities,  the  velocity 
being  greater  the  more  regular  the  channel. 

(105.)  When  a  liquid  in  motion  strikes  a  solid  surface  at  rest, 
or  when  a  solid  surface  in  motion  strikes  a  liquid  at  rest,  the 
quiescent  body  deprives  the  moving  one  of  a  quantity  of  force 
equal  to  that  which  it  receives  ;*  and  this  loss  of  force  is  said 

*  Cab.  Cyc.  Mechanics,  chap.  lv 


CHAP.    IX.  RESISTANCE    OF    FLUIDS.  143 

to  arise  from  the  resistance  which  the  quiescent  body  offers  to 
the  body  in  motion.  When  a  solid  body  is  immersed  in  a  liquid, 
the  force  necessary  to  move  it  with  any  given  velocity  is  found 
to  be  greater  than  that  which  would  be  necessary  to  move  it 
with  the  same  velocity  when  not  immersed :  this  excess  of  force 
arises  Trom  the  resistance  of  the  liquid  to  the  solid,  and  it  is  a 
problem  of  great  practical  importance  to  establish  the  rules  or 
theorems  by  which  this  resistance  may  be  estimated,  and  by 
which  its  laws  may  be  exhibited.  The  same  rules  precisely 
will  be  applicable  to  solid  bodies,  such  as  the  float-boards  of  a 
water-wheel  when  struck  by  the  water  of  a  mill  course.  In  the 
one  case  the  force  to  be  measured  is  called  the  resistance  of 
the  liquid,  and  in  the  other  it  is  denominated  the  percussion  of 
the  liquid.  In  these,  as  in  almost  every  other  part  of  hydraulics, 
theory  lends  but  feeble  aid  to  practice.  There  are  many  effects 
attending  the  operation  of  the  liquid,  whether  in  resisting  or 
communicating  motion,  which,  from  their  nature,  elude  the 
grasp  of  theory,  and  appear  to  be  incapable  of  being  represent- 
ed by  mathematical  or  arithmetical  language  or  symbols :  never- 
theless, there  are  a  few  general  principles  which  may  be  re- 
garded as  approximating  within  a  certain  degree  of  practical 
results,  and  sufficiently  near  them  to  impress  upon  the  memory 
a  general  notion  of  the  phenomena,  if  not  to  be  useful  in  the 
actual  calculations  of  the  engineer. 

Indeed,  the  first  steps  in  generalizing  this  class  of  effects  are 
almost  as  obvious  to  the  most  common  experience  as  their  exact 
determination  is  difficult.  For  example,  if  a  flat  board  of  a  foot 
square  be  moved  in  water  with  a  certain  velocity,  so  that  its  flat 
side  shall  be  presented  in  the  direction  of  its  motion,  a  certain 
resistance  is  felt,  and  a  certain  force  is  necessary  to  keep  it  in 
motion  ;  but  if  the  same  board  be  moved  in  the  direction  of  its 
edge,  it  is  well  known  that  a  much  less  force  will  be  found 
necessary  to  give  it  the  same  velocity  as  in  the  former  case. 
When  the  boatman  plies  his  oar,  he  keeps  the  flat  part  of  the 
blade  presented  in  the  direction  in  which  he  pulls,  at  that  part 
of  the  stroke  at  which  the  greatest  effect  is  produced  in  impell- 
ing the  boat ;  but  when  he  wishes  to  extricate  the  oar  from  the 
liquid,  preparatory  to  another  impulse,  he  turns  the  blade  edge- 
ways towards  the  water,  and  the  resistance,  which  before  was 
powerful,  becomes  immediately  insignificant.  When  the  wings 
of  a  bird  are  spread  for  flight,  the  flat  and  broad  part  of  their 
plumage  is  presented  downwards,  to  give  them  support  from  the 
resistance  of  the  air  in  that  direction,  while  their  edge  is  pre- 
sented forwards,  to  enable  them  to  cleave  the  air  with  as  little 
resistance  as  possible  in  that  direction. 

These  and  like  effects,  which  constantly  fall  under  our  ob- 
servation, indicate  the  general  fact,  that  the  broader  the  surface 


144  A   TP  -ATISE    ON    HYDROSTATICS.  CHAP.  IX. 

presented  in  the  direction  of  the  motion,  the  greater  will  be 
the  resistance.  But  it  requires  more  accurate  and  philosophic 
examination,  to  decide  whether  the  increase  of  resistance  be 
always  in  the  exact  proportion  of  the  increase  of  surface  pre- 
sented towards  the  motion  :  both  theory  and  experience  decide 
this  question  in  the  affirmative.  The  resistance  arises  from 
the  force  which  the  moving  body  must  expend  in  displacing  the 
particles  of  fluid  which  lie  in  its  way :  all  other  things  being 
the  same,  this  force  must  obviously  be  proportional  to  the  num- 
ber of  particles  to  be  displaced  ;  this  number  will  evidently  be 
determined  by  the  magnitude  of  the  surface.  A  flat  board  of 
the  magnitude  of  one  square  foot  displaces  a  certain  quantity 
of  liquid  by  its  motion  ;  one  of  two  square  feet  will  displace 
twice  that  quantity  ;  and,  therefore,  will  require  twice  the  force 
to  keep  it  in  motion ;  or,  in  other  words,  will  suffer  twice  the 
resistance  ;  and  the  same  will  be  true  whatever  be  the  magni- 
tude of  the  surface.  We,  therefore,  conclude  generally  that — 

"When  a  flat  surface  is  moved  perpendicularly  against  a 
fluid,  the  resistance  which  it  suffers  will  increase  or  decrease 
in  the  -same  proportion  as  the  magnitude  of  the  surface  is  in- 
creased or  decreased." 

(106.)  If,  instead  of  being  presented  perpendicularly  to  the 
liquid,  the  surface  be  presented  obliquely  with  respect  to  the 
direction  of  its  motion,  the  resistance  will  be  diminished  on  two 
accounts :  first,  The  quantity  of  liquid  displaced  will  be  less  ; 
and,  secondly,  The  action  of  the  surface  in  displacing  it  will 
have  the  mechanical  advantage  of  an  inclined  plane,  or  wedge, 
so  that,  instead  of  driving  the  liquid  forward,  it  will  in  some 
measure  push  it  aside. 

Let  A  B,Jlg.  72.,  be  the  surface  of  a  solid  moving  in  a  liquid 

Fig.  72. 


in  the  direction  expressed  by  the  arrow.  It  is  evident  that  the 
quantity  of  liquid  displaced  by  the  surface  A  B  is  the  same  as 
that  which  would  be  displaced  by  the  smaller  surface  A  C  mov- 
ing perpendicularly  against  the  liquid.  Let  us  suppose  that 
A  C  is  half  the  magnitude  of  A  B ;  it  follows,  therefore,  that 
the  quantity  of  liquid  which  would  be  displaced  by  A  C  is  half 


CHAP.    IX.  RESISTANCE    OF   FLUIDS.  14& 

that  which  would  be  displaced  by  A  B,  if  it  moved  perpendicu- 
larly against  the  liquid.  Hence  it  may  be  inferred,  that  by 
reason  of  the  oblique  position  of  A  B^  the  quantity  of  liquid 
which  it  displaces  is  reduced  one  half. 

Again,  this  reduced  quantity  of  liquid  which  is  so  displaced,' 
is  not  driven  perpendicularly  before  the  moving  surface.  The 
surface  A  B  acts  on  each  particle  of  the  liquid  as  a  wedge  acts 
in  cleaving  a  piece  of  timber  ;  and,  by  the  principles  of  mechan- 
ics, it  is  established  that  a  power  acting  against  A  C  will  over 
come  a  force  on  the  face  of  the  wedge  greater  than  its  own 
amount  in  the  proportion  of  A  B  to  A  C  ;*  or,  in  the  case 
already  supposed,  that  of  two  to  one.  We,  therefore,  con- 
clude, that  in  the  oblique  position  of  the  surface  A  B,  com- 
pared with  the  same  surface  moving  perpendicularly  against 
the  liquid,  only  half  the  quantity  of  liquid  is  displaced,  and 
that  quantity  only  offers  half  the  resistance  which  the  same 
quantity  would  offer  to  perpendicular  motion  of  the  surface  A  B. 
The  conclusion  is,  that  by  the  obliquity  of  the  surface  A  B  the 
resistance  is  reduced  to  one  fourth  of  its  amount. 

In  like  manner,  if  A  C  were  a  third  of  A  B,  the  resistance 
would  be  reduced  to  one  ninth  of  its  amount.  If  A  C  were  a 
fourth  of  A  B,  the  resistance  would  be  reduced  to  a  sixteenth 
of  its  amount,  and  so  on  ;  the  resistance  being  always  diminished 
in  the  proportion  of  the  square  of  the  back  of  the  wedge,  as 
compared  with  its  face. 

In  trigonometry,  the  number  which  expresses  the  proportion 
of  A  C  to  A  B  is  called  the  sine  of  the  angle  at  B ;  and  thus 
the  resistance  to  a  surface  moving  in  a  liquid  is  said  to  increase 
or  decrease  in  proportion  to  the  square  of  the  sine  of  the  angle 
which  the  direction  of  the  surface  makes  with  the  direction  in 
which  it  is  moved. 

The  resistance  here  determined  is  that  which  acts  perpen- 
dicularly on  the  surface  A  B.  The  portion  of  it  which  acts  in 
tiie  direction  of  the  motion  may  be  found  by  the  principles  for 
the  resolution  of  force.  Let  D  E  express  the  resistance  per- 
pendicular to  A  B,  and  let  E  F  be  drawn  perpendicular  to  the 
direction  of  the  motion,  D  F  will  express  that  part  of  the  resist- 
ance which  acts  against  the  motion.  The  proportion  of  D  F  to 
D  E  is  the  same  as  that  of -A  C  to  A  B.f 

(107.)  We  have  hitherto  omitted  the  consideration  of  the 
effect  produced  upon  the  resistance  of  the  fluid  by  any  change 
in  the  velocity  with  which  it  strikes  the  solid,  or  with  which 
the  solid  strikes  it.  If  a  flat  board  be  moved  perpendicularly 
against  a  liquid,  it  is  quite  evident  that  the  greater  the  velocity 
with  which  it  is  moved,  the  greater  will  be  the  resistance  which 
the  liquid  will  offer  to  it ;  and  this  effect  may  in  part  be  ac- 

*  Cab.  Cyc.  Mechanics,  chap.  xvi.  t  Ibid.  chap.  v. 

13 


*46  A  TREATISE    ON    HYDROSTATICS.  CHAP.  IX. 

counted  for  very  obviously.  It  has  been  already  explained,  that 
the  resistance  arises  from  the  force  which  the  solid  loses  in 
giving  motion  to  the  liquid  which  stands  in  its  way.  It  is  clear 
that  the  more  rapid  the  motion  of  the  solid  is,  the  greater  will 
be  the  velocity  which  it  will  communicate  to  the  fluid,  and, 
therefore,  the  greater  the  force  with  which  the  fluid  will  be 
propelled  ;  and,  by  consequence,  the  greater  will  be  the  resist- 
ance opposed  to  the  solid.  But  the  increase  of  resistance  is 
not  merely  in  proportion  to  the  velocity.  Each  particle  of  the 
fluid  which  the  solid  strikes  during  one  second  of  time,  if  it 
moves  with  a  double  speed,  receives  from  it  a  double  force,  and 
therefore  offers  to  it  a  double  resistance.  But,  besides  this  the 
circumstance  of  the  body  moving  with  a  double  speed  causes  it 
to  strike  twice  as  many  particles  in  a  second ;  each  particle  as 
just  stated,  being  struck  with  a  double  force.  It  is,  therefore 
apparent  that  a  double  speed  will  cause  the  body  to  impart  a 
fourfold  force  to  the  liquid  which  it  puts  in  motion.  It  will  put 
double  the  quantity  of  liquid  in  motion  with  a  double  velocity  • 
it  follows,  therefore,  that  it  will  be  opposed  by  a  fourfold 
resistance. 

By  like  reasoning,  it  will  be  easy  to  prove  that  a  threefold 
velocity  will  produce  a  ninefold  resistance;  that  a  fourfold 
velocity  will  cause  the  resistance  to  be  increased  sixteen  times, 
and  so  on  ;  the  resistance  varying  in  proportion  to  the  square 
of  the  velocity. 

(108.)  In  the  preceding  investigation  we  have  explained  how 
the  quantity  of  resistance  is  varied  by  any  change  in  the  mag- 
nitude or  figure  of  the  solid,  or  in  the  velocity  with  which  it  is 
moved.  But,  in  order  to  render  these  conclusions  useful  it  will 
be  necessary  to  show  the  actual  amount  of  the  resistance  in 
some  one  particular  case.  If  this  be  known,  its  amount  in  all 
other  cases  may  be  calculated  by  the  theorems  just  explained, 
llius,  if  the  absolute  resistance  produced  by  any  particular 
velocity  be  known,  the  resistance  which  would  be  produced  by 
any  other  velocity  may  be  computed  from  the  established  prin- 
the  vel  '  resistance  varies  in  proportion  to  the  square  of 

Experiments  were  instituted  by  Bossut,  with  a  view  to  de- 
,ennme  the  absolute  resistance  sustained  by  a  solid  moved  in  a 
liquid.  By  these  experiments  it  was  found  that  if  a  flat  board 
were  moved  perpendicularly  against  a  liquid,  it  would  suffer  a 
resistance  equal  to  the  weight  of  a  column  of  the  fluid,  the  base 

JSfSs^iSff  t0  lh\board'  and  the  height  of  which  is  equal 

to  the  height  from  which  a  body  should  fall,  in  order  to  acquire 

the  velocity  with  which  the  board  is  moved  against  the  liquid. 

It  follows  from  this,  that  the  resistance  of  different  fluids Twill 

De  different  according  to  their  specific  gravities,  for  the  heavier 


CHAP.    IX.  FORM    OF    BIRDS   AND   FISHES.  147 

a  column  of  the  same  height  is,  the  greater  in  the  same  pro- 
portion will  the  resistance  be.  Thus  the  resistance  of  sea 
water  is  greater,  in  a  slight  degree,  than  that  of  fresh  water ; 
and  the  resistance  of  mercury  is  many  times  greater  than 
either. 

When  a  jet  of  liquid  strikes  a  solid  at  rest,  it  is  found  that 
the  absolute  resistance  is  different,  but  that  its  variation  depends 
upon  the  same  laws.  In  this  case  the  force  sustained  by  the 
solid  is  equal  to  the  weight  of  a  column  of  the  liquid,  whose 
height  is  double  the  height  from  which  a  body  should  fall  to 
acquire  the  velocity.  Hence  it  follows,  that  a  vein  of  liquid 
striking  a  solid  with  a  certain  velocity  produces  an  effect 
amounting  to  double  that  which  would  be  produced  by  moving 
the  solid  with  the  same  velocity  in  a  similar  liquid  at  rest. 

(109.)  The  theorems  just  established  constitute  the  only 
results  in  hydraulics  which  deserve  the  name  of  general  princi- 
ples, and  which  approximate  within  a  limit  sufficiently  close  to 
the  actual  phenomena  to  be  of  any  practical  utility.  But,  even 
in  the  application  of  these,  there  are  several  circumstances 
which  ought  to  be  taken  into  consideration,  in  restricting  and 
modifying  the  conclusions  deduced  from  them.  They  are,  how- 
over,  attended  with  several  consequences  which  experience 
fully  verifies,  and  which  are  of  considerable  importance  in  the 
practical  applications  of  the  science.  f 

The  effect  produced  on  the  resistance  of  a  liquid  by  the  obli- 
quity of  the  surface  of  the  solid  which  moves  through  it,  forms 
a  prominent  element  in  the  problem  for  determining,  under  dif- 
ferent conditions,  the  shape  of  the  solid.  This  consideration 
must  materially  affect  the  shape  to  be  given  to  vessels  of  all 
denominations,  whether  for  navigating  the  seas,  or  for  inland 
transport  by  canals  and  rivers.  It  is  this  principle  which  causes 
the  length  of  the  vessel  to  be  presented  in  the  direction  of  the 
motion,  and  which  gives  a  sharp  prow,  where  circumstances 
admit  it,  the  advantage  over  a  round  one.  The  boats  which 
ply  on  rivers,  or  other  sheets  of  water  not  liable  to  much  agita- 
tion, nor  intended  to  carry  considerable  freight,  are  so  con- 
structed, that  every  part  of  their  bottom  which  encounters  the 
liquid  moves  against  it  at  an  extremely  oblique  angle.  The 
boats  for  the  conveyance  of  persons  to  short  distances  on  the 
Thames,  and  other  rivers,  afford  obvious  examples  of  this. 

Art  in  these  cases  only  imitates  nature.  Animals,  to  whose 
existence  or  enjoyment  a  power  of  easy  and  rapid  motion  in 
fluids  is  necessary,  have  been  created  in  a  form  which,  with  a 
due  regard  to  their  other  functions,  is  the  best  adapted  for  this 
end.  Birds,  and  especially  those  of  rapid  flight,  are  examples 
of  this. »  The  neck  and  breast  tapering  from  before,- and  in- 
creasing by  slow  degrees  towards  the  thicker  part  of  the  body, 


A   TREATISE    ON   HYDROSTATICS.         CHAP.    IX. 

| 

cause  them  to  encounter  the  air  with  a  degree  of  obliquity 
greatly  diminishing  the  resistance,  slight  as  it  is,  which  that 
attenuated  fluid  opposes  to  their  flight;  but  we  find  a  more 
striking  illustration  of  the  same  principle  in  the  forms  of  fishes 
of  every  denomination.     The  reader  must  not,  however   be 
tempted  to  indulge  in  the  supposition  that  nature  has  in  these 
cases  solved  the  celebrated  problem,  to  find  the  form  of  the 
solid  of  least  resistance.     The  solid  contemplated  in  that  prob- 
lem has  no  other  function  to  discharge  except  to  oppose  the 
resistance  of  the  fluid,  and  the  question  is  one  of  a  purely  ab- 
stract nature,  viz.    What  shape  shall  be  given  to  ab^dy,  so  that 
while  its  volume  and  surface  continue  to  be  of  the  same  mag- 
mtude,  it  will  suffer  the  least  possible  resistance  in  moving 
through  a  fluid  ?     It  will  be  apparent  that  many  conditions  must 
enter  into  the  construction  of  an  animal,  corresponding  to  its 
various  properties  and  functions,  independently  of  those  in  vir- 
tue of  which  it  impels  itself  through  the  deep,  or  cleaves  the 
air.     I  he  detection  of  verifications  of  the  results  of  theory  in 
e  works  of  nature  is  in  general  so  seductive,  that  writers  are 
sometimes  tempted  to  overlook  the  inevitable  causes  of  discrep- 
ancy m  their  eagerness  to  seize  upon  analogies  of  this  kind 
Without,  however,  seeking  in  natural  objects  the  exact  solution 
of  a  mathematical  problem  unencumbered  by  various  conditions 
which  nature  has  to  fulfil,  the  examples  which  have  been  pro- 
duced give  abundant  manifestation  of  design  in  the  works  of 

£liS^T\W^Ch  i8'  °r  u^  t0  be'  the  chief  source  of  the 
delight  which  attends  such  illustrations. 

(110.)  i  The  resistance  arising  from  the  quantity  of  fluid  dis- 

placed by  the  moving  body  may,  therefore,  be  always  greatly 

diminished  and  m  some  cases  rendered  almost  insignificant  bv 

a  proper  adaptation  of  its  shape.*     The  accumulated  resistance 

arising  from  the  increased  speed  of  motion  is,  however,  an  im- 

pediment which  no  art  can  remove.     The  fact  that  the  resist- 

ance of  a  liquid  to  a  body  moving  in  it  increases  in  a  prodi- 

giousjy  rapid  proportion  in  respect  of  the  increase  of  velocity, 

s  one  which  sets  an  impassable  limit  to  the  expedition  of 

transport  by  vessels  moving  on  the  surface  of  water      This 

property  has  long  been  well  known  ;  but  it  has  received  greatly 

increased  importance  from  the  recent  improvements  in  the  ap- 

plication of  steam.     If  a  certain  power  be  required  to  impel  a 

vessel  at  the  rate  of  five  miles  an  hour,  it  might  at  first  view  be 

ought  that  double  that  power  would  cause  it  to  move  at  the 


the  hydrostauc  pressure  of  the  higher  column  at  the  anterior  •  exS£ityS 


CHAP.  IX.       RAIL  ROADS  AND  CANALS.  149 

rate  of  ten  miles  an  hour ;  but  from  what  has  been  already 
proved,  it  will  be  perceived  that  four  times  the  power  is  neces- 
sary to  produce  this  effect.  In  like  manner,  to  cause  the 
vessel  to  move  at  the  rate  of  fifteen  miles  an  hour,  or  to  give 
it  three  times  its  original  speed,  nine  times  the  original  power 
is  necessary.  Thus  it  follows,  that  the  expenditure  of  the 
moving  principle,  whether  it  be  the  power  of  a  steam  engine 
or  the  strength  of  animals,  increases  in  a  much  larger  ratio 
than  the  increase  of  useful  effect.  If  a  boat  on  a  canal  be 
carried  three  miles  an  hour  by  the  strength  of  two  horses,  to 
carry  it  six  miles  an  hour  would  require  four  times  that  number, 
or  eight  horses.  Thus  double  the  work  would  be  executed  at 
four  times  the  expense. 

(111.)  These  considerations  place  in  a  conspicuous  point  of 
view  the  advantages  which  transport  by  steam  engines  on  rail 
roads  possesses  over  the  means  of  carriage  famished  by  in- 
land navigation.  The  moving  power  has  in  each  case  to  over- 
come the  inertia  of  the  load ;  but  the  resistance  on  the  road, 
instead  of  increasing  as  in  the  canal  in  a  faster  proportion  than 
the  velocity,  does  not  increase  at  all.  The  friction  of  a  carriage 
on  a  rail  road,  moving  sixty  miles  an  hour,  would  not  be  greater 
than  if  it  moved  but  one  mile  an  hour,  while  the  resistance  in  a 
river  or  canal,  were  such  a  motion  possible,  would  be  multiplied 
3600  times.  In  propelling  a  carriage  on  a  level  rail  road,  the 
expenditure  of  power  will  not  be  in  a  greater  ratio  than  that  of 
the  increase  of  speed,  and  therefore  the  cost  will  maintain  a 
proportion  with  the  useful  effect,  whereas  in  moving  a  boat  on  a 
canal  or  river,  every  increase  of  speed,  or  of  useful  effect,  en- 
tails an  enormously  increased  consumption  of  the  moving  prin- 
ciple. 

But  we  have  here  supposed  that  the  same  means  may  be  re- 
sorted to  for  propelling  boats  on  a  canal,  and  carriages  on  a 
rail  road.  It  does  not,  however,  appear  hitherto  that  this  is  prac- 
ticable. Impediments  to  the  use  of  steam  on  canals  have  hith- 
erto, except  in  rare  instances,  impeded  its  application  on  them; 
and  Ave  are  forced  to  resort  to  animal  power  to  propel  the  boats. 
We  have  here  another  immense  disadvantage  to  encounter. 
The  expenditure  of  animal  strength  takes  place  in  a  far  greater 
proportion  than  the  increase  of  speed.  Thus,  if  a  horse  of  a 
certain  strength  is  barely  able  to  transport  a  given  load  ten 
miles  a  day  for  a  continuance,  two  horses  of  the  same  strength 
will  be  altogether  insufficient  to  transport  the  same  load  twenty 
miles  a-day.  To  accomplish  that,  a  much  greater  number  of 
similar  horses  would  be  requisite.  If  a  still  greater  speed  be 
attempted,'  the  number  'of  horses  necessary  to  accomplish  it 
would  be  increased  in  a  prodigiously  rapid  proportion.  This 
will  be  evident  if  the  extreme  case  be"  considered,  viz.  that 


150  A   TREATISE    ON   HYDROSTATICS.  CHAP.    X. 

there  is  a  limit  of  speed  which  the  horses  under  no  circum- 
stances can  exceed.* 

The  astonishment  which  has  been  excited  in  the  public  mind, 
by  the  extraordinary  results  recently  exhibited  in  propelling 
heavy  carriages  by  steam  engines  on  rail  roads,  will  subside  if 
these  circumstances  be  duly  considered.  The  moving  power 
and  the  resistance  are  naturally  compared  with  other  moving 
powers  and  resistances  to  which  our  minds  have  been  familiar. 
To  the  power  of  a  steam  engine  there  is,  in  fact,  no  practical 
limit ;  the  size  of  the  machine  and  the  strength  of  the  materials 
excepted.  This  is  compared  with  agents  to  whose  powers  na- 
ture has  not  only  imposed  a  limit,  but  a  narrow  one.  The 
strength  of  animals  is  circumscribed,  and  their  power  of  speed 
still  more  so.  Again,  the  resistance  arising  from  friction  on  a 
road  may  be  diminished  by  art  without  any  assignable  limit, 
nor  does  it  sustain  the  least  increase,  to  whatever  extent  the 
speed  of  the  motion  may  be  augmented ;  on  the  contrary,  the 
motion  of  a  vessel  through  a  canal  has  to  encounter  a  resistance 
by  increase  of  speed,  which  soon  attains  an  amount  which 
would  defy  even  the  force  of  steam  itself,  were  it  applicable,  to 
overcome  it  with  any  useful  effect. 


CHAP.  X. 

OF  HYDRAULIC  MACHINES. 

WATER  WHEELS.  -  OVERSHOT.  --  UNDERSHOJ.  --  BREAST.  —  BARKER'S 
MILL.  —  ARCHIMEDES'  SCREW.—  SLUICE  GOVERNOR.  —  CHAIN  PUMP. 

(112.)  THE  term  "  hydraulic  machinery,"  in  its  general 
sense,  is  understood  to  comprise  all  machines  in  which  the 
-force  of  water  is  used  as  a  prime  mover,  and  also  those  in  which 
'other  powers  are  applied  for  the  purpose  of  raising  or  impelling 
er  itself.  Many  of  these  machines,  however,  owe  their  ef- 


ficacy to  principles  and  properties,  the  investigation  of  which 
properly  belongs  to  departments  of  physical  science  foreign  to 
"that  which  forms  the  subject  of  the  present  treatise.  We  shall, 
therefore,  here  confine  our  observations  to  such  machines,  or 
,t>arts  of  machines,  as  admit  of  explanation  by  the  principles  of 

a  ydrostatical  science,  combined  with  the   ordinary  principles 

o/   'mechanics. 

The  most  usual  way  in  which  water  is  applied  as  a 

^-^.fc..  *  Cab.  Cyc.  Mechanics,  cliap.  x*, 


CHAP.    X. 


OVERSHOT    WHEEL. 


151 


prime  mover  to  machinery,  is  by  causing  it  to  act  either  by  its 
impulse  in  motion,  or  by  its  weight  on  the  circumference  of  a 
wheel,  in  a  direction  at  right  angles  to  the  spokes  or  radii,  and 
thus  to  make  the  wheel  revolve  and  communicate  motion  to  its 
axis.  This  motion  is  transmitted  in  the  usual  way,  by  wheel- 
work  and  other  contrivances,  to  the  machinery  which  it  is  re- 
quired to  work. 

Water  wheels  vary  in  their  construction,  according  to  the 
way  in  which  the  force  of  the  liquid  is  intended  to  be  applied 
to  them.  The  principal  forms  which  they  assume  are  denom- 
inated overshot,  undershot,  and  breast  wheels. 

Overshot  Wheel. 

(114.)  The  most  common  form  of  the  overshot  wheel  is  rep- 
resented in  Jig.  73.  On  the  rim  of  the  wheel  a  number  of  cav- 

Fig.  73. 


ities,  called  buckets,  are  constructed,  which  in  the  figure  are 
exposed  to  view,  by  supposing  one  of  the  sides  which  enclose 
them  to  be  removed.  What  may  be  called  the  mouths  of  the 
buckets  are  all  presented  in  one  direction  in  going  round  the 
wheel,  and  by  this  means  the  buckets  on  one  side  will  always 
have  their  mouths  presented  upwards  or  nearly  so,  while  those 
on  the  other  side  will  have  their  mouths  presented  downwards. 
It  follows,  therefore,  that  the  buckets  on  the  side  B  are  in 
such  a  position  that  all  of  them  are  capable  of  containing  some 
water,  and  some  of  them  of  being  kept  filled,  while  those  on 
the  side  D  are  incapable  of  retaining  any  liquid.  Let  us  sup- 
pose a  stream  to  flow  from  F  into  the  bucket  marked  1.  The 
weight  of  the  water  which  fills  this  bucket  will  cause  the  wheel 
to  turn  in  the  direction  1^23,  &c.,  and  the  other  buckets  will 
successively  come  under  the  stream,  and  become  filled ;  and  this 


152  A    TREATISE    ON    HYDROSTATICS.  CHAP.    X. 

continues  until  the  range  of  buckets  from  A  to  B  are  filled.  As 
the  buckets  approach  B  they  begin  slightly  to  lose  the  liquid 
by  their  change  of  position,  and  after  passing  B  this  loss  is 
rapid,  so  that  before  they  arrive  at  the  lowest  point  C,  they  are 
empty,  and  in  that  state  they  ascend  round  C  D  to  A,  where 
they  are  again  replenished.  It  appears,  therefore,  that  there 
is  a  weight  of  water  continually  acting  on  one  side  of  the  wheel, 
distributed  in  the  buckets  from  3  to  8,  and  that  this  weight  is 
not  neutralized  by  any  corresponding  weight  on  the  opposite 
side.  The  wheel  is,  therefore,  kept  continually  revolving  in 
the  direction  A  B  C  D.  A  reference  to  the  properties  of  the 
lever,  or  the  wheel  and  axle,  as  explained  in  Mechanics,*  will 
make  it  apparent  that  the  water  contained  in  the  several  buck- 
ets is  not  equally  efficacious  in  giving  motion  to  the  wheel. 
The  weight  of  the  water  which  fills  the  bucket  1  has  the  same 
effect  in  turning  the  wheel  as  an  equal  weight  acting  down- 
wards at  a  would  have  in  turning  the  lever  D  B  on  the  centre 
O.  In  like  manner  the  weight  of  the  water  in  bucket  2  has  the 
same  effect  in  turning  the  wheel,  as  a  similar  weight  acting  at 
b  would  have  in  turning  the  same  lever  D  B.  Now  if  the 
weights  be  the  same,  the  efficacy  to  turn  the  lever  will  be  in- 
creased in  the  proportion  of  O  a  to  O  b.  Although  the  contents 
of  the  bucket  in  passing  from  1  to  2  may  experience  a  slight 
diminution,  yet  this  loss  is  perfectly  insignificant  compared 
with  the  advantage  of  the  increased  leverage  O  6.  In  like 
manner  the  leverage  continues  to  increase  ;  that  of  the  bucket 
3  being  O  c,  of  4  being  O  d,  and  finally,  the  bucket  5  having 
the  leverage  of  the  whole  radius.  After  passing  below  B  the 
leverage  begins,  on  the  contrary,  to  decrease,  and  continues  to 
decrease  until  it  arrives  at  C.  From  these  circumstances  it  is 
obvious  that  the  efficacy  of  the  wheel  will,  in  a  great  degree, 
depend  on  giving  the  buckets  such  a  form  as  will  cause  them 
to  lose  as  little  water  as  possible  until  they  pass  the  point  B, 
where  they  have  the  greatest  mechanical  advantage.  As  they 
approach  C  the  circumstance  of  discharging  their  contents  be- 
comes of  less  importance  because  of  the  decreasing  leverage. 

Millwrights  have  expended  much  ingenuity  in  contriving 
forms  for  the  buckets,  calculated  to  retain  the  water  in  those 
parts  of  the  circumference  where  its  action  is  most  efficacious, 
and  to  discharge  it  with  facility  and  expedition.  Details  on 
this  subject  would,  however,  be  misplaced  in  the  present 
treatise. 

Numerous  experiments  have  been  made  to  determine  the 
most  advantageous  size  of  overshot  wheels,  and  the  best  veloci- 
ty at  which  they  can  be  worked.  Most  authors  are  of  opinion, 

*  Cab.  Cyc.  Mechanics,  chni>.  xiv 


CHAP.  X.  BEST    VELOCITY.  153 

that  the  diameter  of  an  overshot  wheel  should  never  exceed  the 
height  of  the  fall  of  water  by  which  it  is  impelled ;  but  that  it 
should  be  as  nearly  equal  to  this  as  is  consistent  with  giving 
the  water  sufficient  velocity  on  entering,  the  buckets.  Some, 
however,  think,  that  the  diameter  might  with  advantage  even 
exceed  the  height  of  the  fall.  With  respect  to  the  velocity  of 
the  wheel,  some  maintain  that  the  slower  the  motion  the  greater 
will  be  the  effect ;  while  others  hold  that  there  is  a  certain 
velocity  (of  very  small  amount)  which  will  give  a  maximum  ef- 
fect, and  assert  that  those  who  maintain  the  contrary  opinion 
have  not  carried  their  experiments  to  a  sufficient  extent  to  es- 
tablish the  principle. 

It  requires  little  reflection  to  be  able  to  perceive  how  the 
useful  effect  may  be  greatest  when  the  wheel  moves  with 
a  certain  velocity,  any  increase  or  decrease  of  that  velocity  di- 
minishing the  actual  quantity  of  work  done  in  a  given  time. 
The  power  of  the  wheel  being  the  same,  the  velocity  with 
which  it  moves  will  be  less  in  proportion  as  its  load  is  increased. 
Supposo  a  water  wheel  works  a  flour  mill,  in  which,  at  different 
times,  it  has  to  move  a  different  number  of  millstones,  it  is  evi- 
dent that  the  greater  the  number  it  has  to  move,  the  slower  will 
be  the  motion  which  it  will,  impart  to  each ;  and,  therefore, 
although  the  quantity  of  flour  produced  will  be  increased  by 
increasing  the  number  of  stones,  yet  the  quantity  which  each 
stone  will  produce  will  be  diminished  by  the  increased  slowness 
of  the  motion.  There  is  a  certain  velocity  at  which  these  ef- 
fects mutually  neutralize  each  other,  and  at  this  velocity  the 
useful  effect  is  at  its  maximum. 

Suppose  the  power  of  the  wheel  is  expended  on  moving  the 
millstones  without  being  fed  with  corn ;  the  velocity  of  the 
wheel  will  then  evidently  be  greater  than  if  the  resistance  of 
the  grain  were  opposed  to  the  power.  The  useful  effect  will, 
however,  in  this  case  be  nothing ;  the  whole  power  being  ex- 
pended on  moving  the  unloaded  machine.  Let  one  pair  of 
stones  be  now  called  into  action  ;  the  velocity  will  be  immedi- 
ately diminished  by  the  increased  resistance,  and  the  useful 
effect  will  be  estimated  by  the  quantity  of  flour  produced  by 
the  single  pair  of  stones  in  a  given  time,  as  one  day.  Let  two 
pair  of  stones  be  now  called  into  action ;  the  resistance  being 
further  increased,  the  velocity  will  sustain  a  corresponding 
diminution.  The  first  pair  of  stones  will  produce  a  less  quan- 
tity of  flour  in  a  day  than  they  did  before  the  second  pair  were 
called  into  action ;  but  this  will  be  more  than  compensated  for 
by  the  quantity  of  flour  produced  by  the  second  pair,  which 
before  were  unemployed.  The  same  reason  will  be  applicable 
if  a  third  pair  be  called  into  action,  and  so  on.  Now  it  is  evi- 
dent that  the  wheel  may  be  required  to  move  so  many  pairs  of 


154  A   TREATISE    ON    HYDROSTATICS.  CHAP.    X. 

stones,  that  its  whole  power  will  be  necessary  barely  to  give 
them  motion,  none  remaining  to  overcome  the  additional  resist- 
ance offered  by  the  corn  with  which  they  are  fed.  This  resist- 
ance will  then  stop  all  motion,  and  no  work  will  be  done  or 
useful  effect  produced.  It  is  evident  that  as  the  machine 
gradually  approaches  this  limiting  state,  the  useful  effect  will 
diminish  by  degrees  before  it  altogether  vanishes  ;  and  the 
point  at  which  it  commences  so  to  diminish  is  that  at  which 
the  machine  has  the  velocity  which  produces  the  greatest  use- 
ful effect. 

"  Experience,"  says  Smeaton,  "  proves  that  the  velocity  of 
three  feet  in  a  second  is  applicable  to  the  highest  overshot 
wheels  as  well  as  to  the  lowest ;  and  all  other  parts  of  the 
work,  being  properly  adapted  thereto,  will  produce  very  nearly 
the  greatest  effect  possible.  However,  this  also  is  certain  from 
experience,  that  high  wheels  may  deviate  farther  from  this  rule 
before  they  will  lose  their  power  by  a  given  aliquot  part  of  the 
whole,  than  low  ones  can  be  admitted  to  do.  For  a  wheel 
of  24  feet  high  may  move  at  the  rate  of  6  feet  per  second,  with- 
out losing  any  considerable  part  of  its  power  ;  and,  on  the  other 
hand,  I  have  seen  a  wheel  of  33  feet  high,  that  has  moved  very 
steadily  and  well,  with  a  velocity  but  little  exceeding  2  feet 
per  second." 

Undershot  Wheel. 

(115.)  An  undershot  water  wheel  is  an  ordinary  wheel  turn- 
ing on  an  axis,  furnished  with  a  number  of  flat  boards  placed 
at  equal  distances  on  its  rim,  and  projecting  from  it  in  direc- 
tions diverging  from  its  centre,  and  having  their  flat  faces  at 
right  angles  to  the  plane  of  the  wheel.  These  boards  are  called 
float  boards  ;  and  such  a  wheel,  of  the  most  common  construc- 
'ion,  is  represented  in  Jig.  74.  The  edge  of  the  wheel,  at  its 

Fig.  74. 


lowest  point,  is  immersed  in  a  stream  called  a  mill-course,  and 


CHAP.    X.         UNDERSHOT    AND    BREAST    WHEELS.  155 

the  float  boards  are  intended  to  receive  the  impulse  of  the 
water  as  it  passes  under  the  wheel.  The  wheel  is  thereby 
caused  to  revolve  in  the  direction  of  the  stream,  with  a  force 
depending  on  the  quantity  and  velocity  of  the  water,  and  the 
number,  form  and  position  of  the  float  boards. 

The  mill-course  is  usually  an  artificial  canal,  carried  from 
the  river  or  other  reservoir  from  which  the  wntor  is  supplied, 
and  conducted,  after  it  has  passed  the  wheel,  to  some  con- 
venient point,  where  it  may  be  again  discharged  into  the  bed 
of  the  river.  In  order  that  the  water  may  strike  the  wheel 
with  the  greatest  possible  force,  no  more  inclination  is  given 
to  the  mill-course  A  B,/g".  75.,  than  is  sufficient  to  give  motion 

Fig.  75. 


Ulllllllllllllllllllllll 

uiuuiiuuniiimii 


to  the  water  in  it,  until  it  comes  within  a  short  distance  of  the 
wheel.  There  a  fall  B  F  is  constructed,  and  the  stream  having 
acquired  a  velocity  corresponding  to  the  height  of  this  fall  rushes 
against  the  float  boards,  and  puts  the  wheel  in  motion.  The 
mill-course  then  has  a  further  fall  M  V  N  to  carry  off  the  water, 
which  would  otherwise  impede  the  advancing  float  board. 

It  is  found  by  experience  advantageous  that  the  float  boards 
should  not  precisely  converge  to  the  centre  of  the  wheel,  but 
that  instead  of  being  perpendicular  to  the  rim  of  the  wheel  they 
should  present  an  acute  angle  towards  the  current.  By  this 
means  force  is  gained,  not  merely  by  the  impulse  of  the  water, 
but  in  some  degree  by  its  weight. 

The  experiments  instituted  to  determine  the  best  velocity  of 
the  wheel',  and  the  best  number  of  float  boards,  under  given 
circumstances,  do  not  appear  to  have  led  to  any  principles,  suf- 
ficiently general  and  certain,  to  entitle  them  to  notice  here. 

Breast  Wheel. 

(116.)  A  breast  wheel  partakes  of  the  nature  of  the  overshot 
and  undershot  wheels.  Like  the  latter,  it  is  furnished  with 
float  boards  instead  of  buckets  ;  but,  like  the  former,  it  is  work- 


156  A  TREATISE  ON  HYDROSTATICS.      CHAP.  X. 

ed  more  by  the  weight  of  water  than  by  its  impulse.  The  water 
is  delivered  at  a  point  M,  Jig.  76.,  nearly  on  a  level  with 
the  axis  of  the  wheel,  and  the  mill-course  below  that  point  is 


Fig.  76. 


accommodated  to  the  shape  of  the  wheel,  so  that  the  float 
boards  turn  nearly  in  contact  with  it.  The  spaces  enclosed  by 
the  float  boards  and  the  mill-course  thus  serve  the  same  pur- 
pose as  buckets  in  the  overshot  wheel,  and  the  water  enclosed 
in  them  turns  the  wheel  by  its  weight. 

Barker's  Mill. 

(117.)  The  machine  known  by  this  name  consists  of  a  hollow 
upright  tube  of  metal,  A  B)t%.  77.,  terminating  in  the  upper 
end  B  in  a  funnel,  and  attached  to  an  upright  axis  C  D,  on 
which  a  toothed  wheel  is  fixed,  from  which  motion  may  be 
communicated  to  any  machinery.  The  hollow  tube  B  A  com- 
municates with  a  cross  tube  E  F  closed  at  the  ends,  and  the 
upright  tube  A  is  closed  at  the  lower  end,  and  terminates  in  a 
point  or  pivot,  which  turns  freely  in  a  hollow  cone  adapted  to 
receive  it.  The  whole  is  enclosed  in  a  frame  and  immersed  in 
a  reservoir.  Let  water  be  supposed  to  be  supplied  to  the  fun- 
nel B,  from  a  pipe  G,  and  let  the  upright  and  cross  tubes  be 
thus  filled.  The  water  standing  at  the  level  B,  a  pressure  is 
excited  on  every  part  of  the  cross  tube  E  F  equal  to  the  weight 
of  a  column  of  water  whose  height  is  A  B.  But  since  this 
pressure  acts  equally  in  every  possible  direction  on  the  tube 
ii.  F,  it  will  keep  the  tube  in  equilibrium,  and  no  motion  will 


CHAP.    X. 


BARKER'S  MILL. 


157 


ensue.  Let  two  holes  be  now  pierced  in  opposite  sides  of  the 
tube  E  F,  and  near  the  extremities,  and  let  the  water  be  sup- 
plied at  G  as  fast  as  it  flows  from  these  holes,  so  that  the  level 

Fig.  77. 


B  will  be  maintained.  Those  parts  of  the  tube  E  F,  from  which 
the  water  issues,  will  thus  be  relieved  from  the  pressure  above 
mentioned,  but  the  corresponding  points  on  the  opposite  sides 
of  the  tube  will  still  continue  to  sustain  the  same  pressures. 
These  pressures  are,  therefore,  no  longer  counterbalanced, 
since  they  both  tend  to  make  the  tube  revolve  in  the  same  di- 
rection. The  arms  E  F  will,  therefore,  immediately  commence 
to  revolve,  and  will  turn  the  upright  tube  round  on  the  pivot, 
giving  motion  at  the  same  time  to  the  toothed  wheel  above. 
This  motion  may  be  communicated  to  any  kind  of  machinery. 

In  some  elementary  works  on  hydraulics,  the  operation  of 
this  machine  is  explained  on  totally  wrong  principles.  The 
motion  is  said  to  be  produced  by  the  resistance  of  the  air  to 
the  issuing  water.  It  would  be  easy  to  refute  this  absurd  no- 
tion upon  theoretical  principles  ;  but  perhaps  the  argument 
'most  intelligible  to  those  who  give  such  an  explanation,  is  to 
bid  them  try  a  model  of  Barker's  mill  in  vacuo.  The  motion  is 
produced  on  a  principle  precisely  similar  to  that  which  causes 
a  gun  to  recoil  when  discharged. 

Archimedes'  Screw. 

(118.)  This  instrument  is  said  to  have  been  invented  by  Ar 
14 


158  A    TREATISE    ON    HYDROSTATICS.  CHAP.    X. 

r  •••^•>. 

chimedes  when  in  Egypt,  for  the  purpose  of  enabling  the  in- 
habitants to  clear  the  low  grounds  from  the  stagnant  water 
which  remained  after  the  periodical  overflowings  of  the  Nile. 
It  was  also  used  instead  of  a  pump  to  clear  water  from  the 
holds  of  vessels  ;  and  Athenseus  states  that  the  memory  of  Ar- 
chimedes was  venerated  by  sailors  for  the  benefit  thus  conferred 
on  them. 

The  instrument  may  be  presented  under  different  forms, 
which,  however,  all  agree  in  principle.  Suppose  a  leaden  tube 
to  be  bent  into  a  spiral  form  like  a  corkscrew,  or  the  worm  of  a 
still,  as  represented  in  Jig.  78.  Suppose  A  the  extremity  to  be 

Pig.  78. 


open  and  presented  upwards,  and  suppose  the  screw  to  be 
placed  in  an  inclined  position,  as  represented  in  the  figure. 
From  its  peculiar  form  and  position  it  is  evident  that  commenc- 
ing at  A,  the  screw  will  descend  until  we  arrive  at  a  certain 
point,  B ;  in  proceeding  from  B  to  C  it  will  ascend.  Thus  B 
is  a  point  so  situate  that  the  parts  of  the  screw  on  both  sides  of 
it  are  more  elevated  than  it  is,  and  therefore  if  any  body  were 
placed  in  the  tube  at  B,  it  could  not  move  in  either  direction 
B  A  or  B  C,  without  ascending.  Again,  the  point  C  is  so  situ- 
ate, that  the  tube  on  each  side  of  it  descends ;  and  as  we  pro- 
ceed, we  find  another  point,  D,  which  like  B,  is  so  placed  that 
the  tube  on  each  side  of  it  ascends,  and,  therefore,  that  a  body 
placed  at  D  in  the  tube  could  not  move  in  either  direction 
without  ascending.  In  like  manner  there  are  a  series  of  points, 
F,  H,  &c.,  continued  along  the  whole  length  of  the  spiral, 
which  are  circumstanced  like  B  and  D ;  and  another  series, 
E,  G,  &c.,  which  are  circumstanced  like  C. 

Let  us  now  suppose  a  ball,  less  in  size  than  the  bore  of  the 
tube,  so  as  to  be  capable  of  moving  freely  in  it,  to  be  dropped  in 


CHAP.  x.  ARCHIMEDES'  SCREW.     ,  159 

at  A.  As  the  tube  descends  from  A  to  B  the  ball  will  descend 
by  its  weight,  as  it  would  down  an  inclined  plane,  until  it  ar- 
rive at  B.  The  force  Avhich  it  acquires  in  its  descent  will  carry 
it  beyond  this  point,  and  will  cause  it  to  ascend  to  a  small  dis- 
tance towards  C  ;  but  its  weight  soon  destroys  the  force  which 
it  has  retained  by  its  inertia,  and  after  a  few  oscillations  on  each 
side  of  B,  its  motion  will  altogether  be  destroyed  by  the  friction 
of  the  tube,  and  it  will  remain  at  rest  at  that  point. 

Now  suppose  the  ball  for  a  moment  to  be  fastened  or  attached 
to  the  tube  at  B,  so  as  to  be  incapable  of  moving  in  it ;  and 
suppose  the  screw  to  be  turned  nearly  half  round,  so  that  the 
end  A  shall  be  turned  downwards,  and  the  point  B  brought 
nearly  to  the  highest  point  of  the  curve  ABC.  It  is  evident 
that  the  series  of  points  B,  D,  &c.,  which  were  before  situate 
so  as  to  have  ascending  parts  of  the  tube  on  each  side  of  them, 
are  now  in  the  very  contrary  predicament,  having  interchanged 
situations  with  the  points  C,  E,  &c.,  as  represented  in  Jig.  79. 

Fig.  79. 


The  ball  which  we  supposed  attached  to  the  tube,  is  now  hang- 
ing as  it  were  on  the  brow  of  an  acclivity,  immediately  to  the 
right  of  the  highest  point  at  B ;  for  we  have  supposed  the  point 
where  the  ball  was  placed  to  be  brought  nearly,  but  not  exactly, 
to  the  highest  point.  If  the  ball  be  now  disengaged  or  detach- 
ed, it  will  descend  by  its  gravity  from  B  to  C,  where  it  will 
ultimately  rest.  The  point  at  which  B  was  placed  when  the 
screw  was  in  the  position  represented  in  Jig.  78.,  is  marked  b 
in  Jig.  79.  In  fact,  by  turning  the  screw  on  its  axis  half  round, 
it  must  be  evident,  upon  the  slightest  attention,  that  no  point 
of  it  can  be  really  advanced  in  the  direction  of  its  length,  and 


160  A    TREATISE    ON    HYDROSTATICS.  CHAP.    X. 

that  no  other  effect  can  be  produced  than  to  cause  every  point 
to  revolve  in  a  circle  round  its  axis.  Thus  the  point  B,  Jig.  78., 
is  transferred  from  the  lowest  part  of  the  circle  in  which  it  re- 
volves, nearly  to  the  highest,  as  represented  in  Jig.  79. :  the  ball, 
therefore,  being  no  longer  placed  between  two  ascending  parts 
of  the  screw,  will  no  longer  be  prevented  from  moving  in  obe- 
dience to  its  gravity  ;  it  will  have  an  ascent  on  one  side  and  a 
descent  on  the  other,  and  towards  the  latter,  of  course,  it  must 
fall.  The  whole  effect,  therefore,  of  the  half  turn  which  we 
have  supposed,  is  to  transfer  the  ball  from  the  point  6  to  the 
point  C,  which  is,  in  fact,  equivalent  to  moving  it  up  the  inclined 
plane  A  C,  'Jig.  79.,  from  b  to  C. 

Another  half  turn  of  the  screw  will  be  attended  with  similar 
effects.  The  ball  being  supposed  to  be  attached  to  the  tube  at 
C,  will,  when  the  tube  is  restored  to  the  position  represented 
in  Jig.  78.,  cause  the  ball  to  stand  on  the  brow  of  an  acclivity 
descending  from  C  to  D.  If  the  ball,  therefore,  be  again  disen- 
gaged, it  will  fall  to  D,  where  it  will  again  rest.  By  this  means 
the  ball  is  therefore  carried  up  the  inclined  plane  from  c  to  D, 
as  in  Jig.  78.,  or,  what  is  the  same,  from  C  to  d  in  Jig.  79. 

It  is  clear  that,  by  continuing  this  reasoning,  we  could  show, 
that,  under  the  circumstances  supposed,  the  ball  would  be 
gradually  transferred  from  the  lowest  point  of  the  inclined 
plane  to  the  highest  as  far  as  the  screw  extends. 

We  have  supposed  the  ball  to  remain  attached  to  the  screw 
at  B  until  a  half  turn  of  the  screw  is  nearly  completed,  and  not 
until  then  to  be  detached.  But  suppose  that  the  ball  is  detached 
when  a  very  small  part  of  a  turn  has  been  made  :  the  point  B 
will  thus  be  brought  into  a  situation  a  little  above  that  at  which 
it  has  an  ascending  branch  of  the  screw  on  each  side  of  it ;  it 
will  then  have  a  descending  part  on  that  side  from  which  it  was 
moved ;  if  detached  it  will  consequently  descend  in  that  direc- 
tion, and  will  cease  to  move  when  it  arrives  in  that  part  of  the 
screw  where  it  will  have  an  ascending  branch  at  each  side  of 
it.  Now  suppose  the  ball  not  to  be  attached  to  the  tube,  but 
merely  to  lie  in  it,  the  motion  which  we  have  here  supposed  to 
be  effected  at  intervals,  and  to  be  interrupted  by  the  ball  being 
occasionally  attached  to  the  tube  so  as  to  prevent  it  moving, 
will,  in  fact,  take  place  continuously,  and  the  ball  will  be  car- 
ried up  the  inclined  plane,  not  by  distinct  efforts  separated  by 
intervals,  but  by  one  uninterrupted  and  continuous  motion. 

All  that  has  been  said  of  a  ball  in  the  tube  would  be  equally 
true,  if  a  drop  or  any  quantity  of  a  liquid  were  contained  in  the 
tube  instead  of  the  ball.  Therefore,  if  the  extremity  of  the 
screw  were  immersed  in  a  well  or  reservoir  of  water,  so  that 
the  water  would  by  its  weight  or  pressure  be  continually  forced 


CHAP.  x.  ARCHIMEDES'  SCREW.  161 

into  the  extremity  of  the  tube,  it  would,  by  turning  the  tube, 
be  gradually  carried  along  the  spiral  to  any  height  to  which  it 
may  extend. 

From  the  explanation  given  above  it  is  clear,  that  it  is  essen- 
tial to  the  performance  of  this  machine  that  the  elevation  of  the 
spiral  above  the  horizontal  position  should  not  exceed  a  certain 
limit.  In  fact,  in  each  spire  of  the  tube  a  certain  point  must 
be  found,  on  either  side  of  which  the  tube  ascends.  Now  it  is 
apparent  that  the  tube  may  be  so  elevated  in  its  position,  that 
the  part  of  the  tube  which  proceeds  towards  the  lower  extremi- 
ty of  the  screw  will  descend  in  every  part  of  the  tube :  this 
will  be  quite  evident  if  the  screw  be  supposed  first  to  be  placed 
in  a  perfectly  upright  position.  Under  such  circumstances  it 
is  obvious,  that  if  the  ball  were  placed  any  where  in  the  tube 
it  would  fall  down  to  the  lowest  point ;  a  slight  inclination  from 
the  vertical  position  will  not  prevent  this  from  happening ;  but 
if  the  screw  receive  such  an  inclination,  that  in  each  spire  a 
point  will  be  found  so  placed  that  the  part  proceeding  towards 
the  lower  extremity  shall  ascend,  then  the  ball  placed  at  such 
a  point  will  remain  at  rest ;  and,  if  the  screw  be  turned,  will  as- 
cend, as  already  explained. 

In  practice,  the  spiral  channel  through  which  the  water  is 
carried  is  not  in  the  form  of  a  tube.  A  section  of  the  instru- 
ment, as  ased  in  practice,  is  represented  in  fig.  80. 

Fig.  80. 


The  screw  possesses  an  advantage  over  common  pumps  in 
being  capable  of  raising  water  which  is  not  pure,  being  mixed 
with  gravel,  weeds,  or  sand.  The  screw  may  be  kept  in  a  state 
of  revolution  by  any  of  the  usual  moving  powers.  Dr.  Brewster 
mentions  that  an  excellent  engine  of  this  description  was 
erected,  in  1816,  at  Hurlet  alum  works,  upon  the  water  of  Lev- 
ern  near  Paisley.  This  engine  was  moved  by  a  water  wheel, 
which  communicated  by  a  long  shaft  with  the  screw  ;  a  beveled 
wheel  was  constructed  on  the  screw,  which  worked  in  another 
14* 


Mi;i  A     TI'.i.MI     i:     »\     IIYIUMI-'I    M  [«  »  JI 

beveled    wheel  on  t.he  f>:\  H-mity  of  the  shn.f>.  ;   nnot.her  bev:lod 

whccj    on    |J,<:    .-,v|r:    of  t.he    Wilt  er- wheel,  Worked    ill    a  C01Te»pOll(I- 

intr  wheel  on  t.he  ot.he.r  oxt.re.init.y  of  the  <;h;i.ft..  The  nerew  WII.M 
HIM::  I'. '-pi.  in  r.on.Ht.niit.  revolnfion  by  the  Ihll  of  wnt.er  which  .sup- 
plied (.he  reservoir,  from  wheneo  t.he  ;;;ime  wu.t,er  WII.H  to  be; 
rr.jsed  by  MM:  :-.crew  ilH<;lf. 

7Vic  Sluice  Governor. 

fll!>.j   In   i-v|,|;iiriinrr   f|,i-   oj'«-r:it.ioM  of  w».t.«T   wli»:»:l>:,  it.  was 

rJiovvn  ll,.-it   lli<-,c   w.r:  :i   -  «-rt:nn   v«-lorit.y  ;.t,  wliii-.li  t.lnt  useful  i:f- 

fect  resulting  from  them  is  a  maximum.  Any  deviation  from 
thin  rate  of  motion,  whether  by  increase  or  decrease,  must  ho 
attended  by  a  corresponding  loss  of  power :  but,  since  the  water 
in  the  mill-course  must,  from  obvious  natural  causes,  be  subject 

f.o  coni'.idcrnblr  fliirl.iKit.ioiiH  in  it.n  qimrit.it.y  nwl  forr.i:,  tin:  vHori- 
l.y  which  it  WOUld  Communicate  tO  tin;  wheel  would  nmleiyo 
proportiormt.f:  v/iriat.ioriH.  It.  i;;,  therefore,  nere:;:,;iry  to  j)f(ivn!«- 
siome  mi  "MI  ;  of  coiilj-ollinjf  j.lic  ,j  i  KID  I  it  y  of  w;it.er,  ri.iid  me;i.::nrifi"; 
out.  the  |IOU<T  :  i,  ;,  :  ),,  1 1 1  ;i  i  n  t  ,i  1 1 1  ;i  ::tc;idy  velocity  ill  the  wheel. 
JwlfpfrriuVrjt.ly  of  t.lir:  llnrtnutinjf  nncr^y  ofthe  power,  chnn/n.s 
f)f  velocity  ure  h;ih|e|r,  he  produced  by  occ;,  loiinl  <-h;i /i^e M  in 

the  amount  of  the  load  or  resistance.    Thus,  in  a  com  null,  if 

n.  /'rent.er  or  I-MM  number  of  p;iir:-;  of.':toii'':!  nre  in  ;ict,ion  »t,  otiei 
time  t.linn  nt.  nnother,  n  proporlionnt.ely  increased  or  (/iminished 
•:ii|i|)ly  oft.be  moving-  pow»-r  will  he  nere;,  ;;iry  t.o  i'\\<-  t.he  wheel 
tin-  Hfirne  vr-locity. 

'I'll"    ne«-ei:::ily  of   re.rii|:,|,,,.r    th'-    I  m  .1  ion  of   I  he   w  In  •«  I    rloen 
not,  however,  alone    :in:<e   from    t.he    jidv:mt.;ure   of  rniiHin^   t.lir: 

lliovill.'f  power  l.i  i  produce  (he  ;n-e;,|e,  t.  jiof.'-ildi!  effect.  The 
IKiture  of  t.he  v.'ork  t.o  he  perfoimed  |  :  ;ilmo:.t  III  every  c;i:-:e  Hildi 
m  re(|iiire;i  (he  ni;iclnn<4ry  t.o  be  moved  with  ;i  cerhiin  velocity. 
Tim,  in  :\.  corn  null,  if  the  r.peed  Mirp;i  .:  ;i  cert;un  limit,  th<: 

flour   heconie.H    heilt.ed    Iilld    lll|UI'''d.        Spllltllll"'  tilld    \ve;i\'inir    in;i 
clunciy,  in    lil.e    iiurUM'T,  n •i|inr«-:.  |()  be  coiidnct.c-d    ;it   ;i.  cr:rt,»in 
rnl.c,  nny  irn^ularity  in  \vhi.-h  must,  injure  or 'lestroy  t.lie  fnhri'-, 
of  lip-  m;iiml;ictiin-. 

I''or  Jill   the;-:e   re;i::oir\  the   power,  w  hrit « •  \  rr  |!    be,  \vhicli   | 
inot.ion  t.o  mncliineM  or  f;ictori'-M,  mii::l.  he  so  re/mhiicd,  JIM,  under 

every  change  of  circumstances,  to  produce  a  uniform  motion ; 

find  t.he  snine  font  riv;mce,  iiMiinlly  c;ill<-d  n .  <n,wninr,  h;in  been 
found  U)  bo  applicable  to  moving  power:,  dilf-  •i\\\«  very  much 
m  tin  'ir  ritilnre,  such  ;IM  v.nl  .-r,  hlesim,  A- rr.  This  in:  1 1  •iiim-iil. 
JiriM  nlrendy  lieen  described  in  the  trentise  on  Mcchiinics  in 
l.lii.-:  (  lyrlopdffin,  m  1 1.  ;  :ippli«-;ilion  to  the  :  !--;im  (  ;-.iii<-.  II  mny 

*   ('-,:  I,  Oil  If.   SVl, 


CHAP     » 


HI, DM   I.     (11 


103 


iidl.   li«-    muni'  i<      I  in;'     In  M   t     I,,,  n     il  |   ;i|,|.l|.  fili'.ii 

III    H-1-lll.ilin."     Ill-'    Ml'. I  101  |l'|      Win    <-|. 

I  >   I ),    //••.  Hi.,  |;1  M.   i-.l  i  nit.  I')   wln«  li   li 

I    I'    li'    -I    ,     I'. Mini      Dili     wlll-l'l    il     K,|H-     I   •    I    ilMH-il,     V.'lil'    II     I        IIIOVI    'I     I'1/ 

ii  <  'MM     |.'.M'lni"    vvlicd1    ji|;i<  ••'!    •  'i. ill    111   III'     mil'  IMII'  iy 

/ ,     II 


ni'iV'l  Ity  Hi'-  \vnld-  v.  li'-'-l.       I'  I',  ;M'-    I---,  li»-;ivy  Imlh  ntlrx  li< d 

I')    I  <>''  ,    :>      J'. Mil    III      I  .          'Mi'       '        ,i|i      'i,i, 

n«  <  i'-'i  i.y  joini        :        Lh  other  rod    ' '  i '      hi<  ii  nrfl  i'.mi«-'i 

MJ.'.M    ii     rin^    nl.    I 
Tin  '    : 


v/ii'    i    t  li<<   • 


rnnii     i  I  I 

(oil:,   A 

«  |nl«  ii    <  I    i  -.    i 
IM/M    with', Ml    • 

"  I'Hj^hl'iu 


y 


)  i     «i  r:iv 

<:a,Uff(r  Hi'-   i  in-/  lit'. 


I'.nit.-i 
•'  I)  |> 

I  .    -     I  ul 

I,:;.     ;,l 

'I'.Mllkrlul,),,., 
'.    Mil    \'>   lilfii    I;'-!'/     '.villiMi     it. 

iipm.  ,i    j  , 

ji    HI     ilo  \  ||,    i.  /  ,    ,l     .  ;,i,,,.,l 

wj1.li  il         T».«-    '-II'-'  I. 
'•  -cnl»'-<l  i».  «-vi'ldil. 

»!    I'M,  Hi 

•    .       ;. 


i    n  ,;,  •-.•  !,  and 

.  tliu    i-  rai  -  -I.     li; 


1(54 


A    TREATISE    ON    HYDROSTATICS. 


CHAP.    X. 


on  the  other  hand,  the  balls  B  B  be  brought  nearer  the  axis, 
the  contrary  effects  will  be  produced,  the  extremity  I  being 
raised,  and  the  extremity  A  lowered.  In  the  one  case  the  fork 
A  will  raise  the  clutch,  and  in  the  other  will  lower  it,  causing 
it  to  slide  along  the  shaft  L  L.  On  this  shaft  are  placed  two 

Fig.  81. 


beveled  wheels  O  P  which  move  loosely  upon  it,  turning  inde- 
pendent of  the  shaft.  A  third  beveled  wheel  R  works  in  both 
of  these,  turning  them  in  opposite  directions.  This  wheel  re- 
ceives its  motion  from  the  shaft  D  D,  with  which  it  is  connected 
by  other  wheels  not  represented  in  the  figure.  Under  the  cir- 
cumstances here  explained,  the  shaft  L  L  is  at  rest,  having  the 
beveled  wheels  O  P  turning  freely  on  it  in  opposite  directions, 
and  the  machinery  is  supposed  to  be  moving  with  the  proper 
velocity. 

Now  suppose  this  velocity  from  any  cause  to  undergo  a  sud- 
den increase.  By  reason  of  the  increased  centrifugal  force 
arising  from  the  whirling  motion,  the  balls  B  B  will  recede 
from  the  shaft  D  D,  and,  as  already  explained,  will  cause  the 
clutch  Q,  to  rise  towards  the  beveled  wheel  P.  This  clutch 
bears  four  projecting  pieces  on  the  face  presented  towards  the 
beveled  wheel,  which  are  pressed  by  the  end  A  of  the  lever 
into  corresponding  cavities  in  that  wheel.  When  this  takes 


CHAP.    X.  CHAIN    PUMP.  165 

place,  the  clutch  is  compelled  to  revolve  with  the  wheel,  and 
the  axis  revolves  with  the  clutch. 

Again,  let  it  be  supposed  that  the  velocity  of  the  machinery 
becomes  diminished,  from  any  cause.  The  centrifugal  force 
produced  by  the  whirling  motion  of  the  balls  B  B  being  thus 
diminished,  the  balls  will  have  a  less  tendency  to  recede  from 
the  axis  D  D,  and  will  therefore  fall  towards  it :  this,  as  already 
explained,  will  cause  the  extremity  of  the  lever  A  to  move  down- 
wards on  the  shaft  L  L,  and  projecting  pieces  on  the  opposite 
face  of  the  clutch  Q,  will  fall  into  cavities  on  the  beveled 
wheel  O,  in  the  same  manner  as  already  described  with  respect 
to  the  beveled  wheel  P.  The  clutch  Q,  and  the  shaft  L  L, 
will  now  be  compelled  to  revolve  with  the  wheel  O,  in  a  direc- 
tion opposite  to  that  in  which  it  revolved  in  the  former  case. 
It  will  therefore  be  perceived  that  any  deviation  in  the  velocity 
of  the  machinery  from  that  velocity  which,  from  its  nature,  it 
ought  to  have,  will  cause  the  shaft  L  L  to  turn  in  the  one  di- 
rection or  in  the  other,  according  as  the  motion  is  increased  or 
slackened.  This  shaft  communicates  by  means  of  an  endless 
screw,  with  a  rack  or  toothed  arch,  which  works  a  sluice  gate, 
as  represented  in  the  figure  ;  and  when  the  shaft  is  turned  in 
one  direction,  it  closes  the  gate  so  as  to  diminish  the  supply  of 
water,  and  when  it  is  turned  in  the  opposite  direction,  it  opens 
the  gate  so  as  to  increase  its  supply.  Thus,  when  the  machine-1 
ry  receives  an  undue  increase  of  speed,  the  sluice-gate  is 
closed,  and  the  supply  of  power  diminished,  and  the  velocity 
checked ;  when  the  motion  is  reduced  to  its  proper  rate,  the 
balls  B  B  fall  to  their  proper  distance  from  the  axis,  and  disen- 
gage the  clutch  from  the  beveled  wheels,  and  all  further  action 
upon  the  sluice-gate  is  stopped.  When  the  machinery  receives 
an  undue  diminution  in  its  rate  of  motion,  the  same  effect  is 
produced  by  the  other  beveled  wheel  opening  the  flood-gate. 
When  the  proper  rate  of  motion  is  restored,  the  balls  B  B  rise 
to  their  first  position  and  disengage  the  clutch. 

Thus  the  machinery  is  constantly  caused  to  move  at  a  uni- 
form rate,  and  the  governor  is  adjusted  in  the  first  instance  so 
that  the  clutch  shall  be  disengaged  from  both  beveled  wheels 
when  the  machinery  is  moving  at  the  proper  rate. 

The  Chain  Pump. 

(120.)  The  chain  pump  is  a  contrivance  for  lifting  water  in  a 
cylinder  by  having  a  movable  bottom  fitting  water-tight  in  it, 
which  can  be  moved  to  the  top,  driving  all  the  contents  of  the 
cylinder  before  it.  In  fig-  82.  A  B  is  a  cylinder,  the  lower  part 
of  which  is  immersed  in  a  well  or  reservoir,  and  the  upper  part 


166 


A    TREATISE    ON    HYDROSTATICS.          CHAP.    X. 


enters  the  bottom  of  a  cistern  into  which  the  water  is  to  be 
raised.  An  endless  chain  is  carried  round  the  wheel  at  the  top, 
and  is  furnished  at  equal  distances  with  pistons  or  movable 
bottoms,  which  fit  water-tight  in  the  cylinder.  As  these  suc- 

Fig.  82. 


cessively  enter  the  cylinder,  they  carry  the  water  up  before 
them,  which  is  discharged  into  the  cistern  at  the  mouth  of  the 
cylinder  above.  The  moving  power  is  usually  applied  by  a 
winch  or  otherwise  to  the  wheel.  The  cylinder  may  be  placed 
in  an  inclined  position,  in  which  it  works  to  more  advantage 
than  when  vertical.  The  effect  is  greatest  when  the  distance 
between  the  pistons  is  equal  to  their  diameters. 


TREATISE 


PNEUMATICS 


A 
TREATISE 

ON 


PNEUMATICS. 


CHAP.  I. 

INTRODUCTION. 

FORM  OF  BODIES.— HOW  AFFECTED  BY  HEAT.— AERIFORM  STATE. — 
ELASTICITY.— DIVISION  OF  MECHANICAL  SCIENCE. — COMPRESSIBILI- 
TY AND  INCOMPRESSIBILITY. — PERMANENTLY  ELASTIC  FLUIDS. — 
VAPOR.— STEAM.— ATMOSPHERIC  AIR. 

(121.)  THE  effects  which  the  presence  of  heat  produces  on 
the  physical  state  of  a  body  have  been  noticed  in  the  first  chap- 
ter of  our  treatise  on  Hydrostatics.  The  opposite  principles  of 
cohesion  and  repulsion  are  made  to  change  their  relation  by  the 
variation  which  the  latter  undergoes  on  the  increase  or  diminu- 
tion of  the  heat  contained  in  the  body.  The  liquid  state  in 
which  bodies  are  contemplated  in  hydrostatics  is  one  in  which 
these  antagonist  principles  are  maintained  in  equilibrium,  or 
nearly  so.  In  the  department  of  physics,  which  we  are  now 
about  to  investigate  and  explain,  bodies  are  contemplated  in 
that  state  which  results  from  the  predominant  influence  of  tho 
repulsive  principle.  The  constituent  particles  of  the  body 
under  consideration  repel  each  other  so  actively,  that  they  fly 
asunder  and  separate,  so  that  the  whole  mass  will  dilate  itself 
to  any  extent,  unless  its  expansion  be  limited  by  the  operation 
of  adequate  forces,  confining  it  within  certain  dimensions. 

The  most  obvious  and  familiar  example  of  the  physical  state 

here  referred  to,  is  that  of  atmospheric  air.    Let  A  B,  Jig.  1., 

be  a  cylinder  in  which  a  piston  P  moves  air-tight,  and  let  us 

suppose  that  a  small  portion,  as  a  cubic  inch,  of  atmospheric  air, 

15 


170 


A   TREATISE    ON    PNEUMATICS. 


CHAP.  I. 


Fig.  \.  in  its  common  state,  be  contained  between  the 
piston  and  the  bottom  of  the  cylinder  :  suppose 
the  piston  now  drawn  upwards,  as  in  Jig.  2.,  so 
as  to  increase  the  space  below  it  to  two  cubic 
inches.  The  air  will  not  continue  to  fill  one 
cubic  inch,  leaving  the  other  cubic  inch  unoc- 
cupied, as  would  be  the  case  if  a  solid  or  liquid 
had  been  beneath  the  piston  in  the  first  in 
stance  ;  but  it  will  expand  or  dilate  until  it 
spread  itself  through  every  part  of  the  two  cubic 
inches,  so  that  every  part,  however  small  of  this 
space,  will  be  found  occupied  by  air.  Again, 
suppose  the  piston  further  elevated,  so  that  the 
p  space  below  it  shall  amount  to  three  cubic 
inches;  the  air  will  still  further  expand,  and 
will  spread  itself  through  every  part  of  the  in- 
creased  space  ;  and  the  same  effect  would  con- 
tinue to  be  produced,  to  whatever  extent  the 
space  might  be  increased  through  which  the  air  is  at  liberty  to 
circulate. 

This  quality  of  expanding,  as  the  surround- 
Fig.  2.  ing  limits  are  enlarged,  has  caused  air,  and 
every  body  existing  in  that  state  which  gives  it 
the  like  property,  to  be  called  an  elastic  fluid  ; 
and,  in  contradistinction  to  this,  liquids  whose 
particles  do  not  repel  each  other,  so  as  to  produce 
the  same  effect,  are  called  inelastic  fluids. 
Thus  the  mechanical  theory  of  inelastic  fluids 
forms  the  subject  of  HYDROSTATICS,  and  that 
of  elastic  fluids  the  subject  of  PNEUMATICS. 
As  water,  the  most  common  of  liquids,  is  taken 
as  the  type  or  example  of  all  others,  the  name 
Hydrostatics  is  taken  from  two  Greek  words, 
signifying  water  and  equilibrium.  In  like  man- 
ner,  air  being  selected  as  the  most  familiar 
example  of  all  elastic  fluids,  the  name  Pneuma- 
tics is  borrowed  from  a  Greek  word  signifying 
azV,  or  breath. 

(122.)  The  qualities  depending  on  the  aeri- 
form state  cannot  properly  be  taken  as  the  basis 
of  the  classification  of  the  species  of  bodies, 
because,  by  the  agency  of  heat,  all  bodies  may  be  reduced  to 
this  state  ;  and  although  in  every  instance  the  question  has  not 
been  brought  to  the  actual  test  of  experiment,  yet  there  are  the 
strongest  analogies  in  support  of  the  conclusion,  that  all  aeriform 
bodies,  including  the  atmosphere  itself,  are  capable  of  being 
reduced  to  the  liquid,  and  even  to  the  solid  form.  We  are, 


CHAP.  I.  .  AERIFORM    STATE.  171 

therefore,  to  regard  the  properties  investigated  in  the  three 
branches  of  physical  science  respecting  solids,  liquids,  and 
gases,  not  as  peculiar  properties  of  distinct  species  of  bodies, 
but  as  qualities  which  will  appertain  to  all  bodies  whatsoever, 
according  as  they  are  affected  by  certain  external  agencies. 

Water  affords  a  convenient  example  of  the  truth  of  these 
observations.     In  the  state  of  ice,  its  properties  come  under  the 
dominion  of  mechanics,*  commonly  so  called.    When  exposed 
to  temperatures  which  no  longer  permit  its  existence  in  the 
solid  state,  it  loses  s*bme  of  those  properties,  and  acquires  others, 
which  hand  it  over  to  the  sway  of  Hydrostatics.     A  further 
increase  of  temperature  will  cause  it  to  pass  into  the  state  of  ; 
vapor  or  steam,  and  impart  to  it  those  qualities  which  appropri-  J 
ate  its  investigation  to  Pneumatics. 

Since,  by  imparting  heat  continually  to  a  body,  it  is  made  to  • 
pass  successively  from  the  solid  to  the  liquid,  and  from  the  • 
liquid  to  the  gaseous  state,  and  by  continually  abstracting  heat 
it  may  be  transferred  in  the  contrary  direction  from  the  gaseous 
to  the  liquid,  and  from  the  liquid  to  the  solid  state,  it  might, 
perhaps,  be  inferred  that  all  bodies  in  the  solid  state  must  be 
colder  than  those,  in  the  liquid,  and  all  liquids  colder  than  bodies 
in  the  gaseous  state.     Such  an  inference,  however,  may  be 
proved  to  be  unfounded  in  two  ways. 

1.  Bodies  of  different  kinds  pass  from  the  one  to  the  other  of 
these  states  at  different  temperature;  thus,  to  cause  water  to 
pass  from  the  liquid  to  the  solid  state,  it  is  necessary  to  reduce 
its  temperature  to  32°  of  the  common  thermometer ;  but  if  we 
wonH  reduce  quicksilver  from  the  liquid  to  the  solid  state,  a 
much  more  diminished  temperature  must  be  produced.     Thus 
it  may  be  perceived  that  water  in  the  solid  state  may  be  at  a 
much   higher  temperature  than  mercury  in  the  liquid  state. 
Again,  to  cause  water  to  pass  from  the  liquid  to  the  gaseous 
state,  it  is  necessary,  under  ordinary  circumstances,  to  raise  its 
temperature   to  212°  of  the  common  thermometer.     Now  to 
cause  mercury  to  pass  from  the  liquid  to  the  gaseous  state 
would  require  its  temperature  to  be  raised  to   above   650°. 
Hence  it  appears  that  water  in  the  aeriform  state  may  have  a 
much  lower  degree  of  heat  than  mercury  in  the  liquid  state ; 
but, 

2.  The  error  that  we  have  just  noticed  arises  partly  from  the 
supposition  that  all  the  heat  which  a  body  contains  is  in  a  state 
to  affect  the  senses  or  the  thermometer.     In  other  words,  it  is 

*  In  the  correct  application  of  the  term,  MECHANICS  includes  the  doctrines  of 
equilibrium  and  motion  of  bodies  in  all  the  three  states  of  solid,  liquid,  and  gas  ; 
hut  its  more  popular  and  vulgar  application  is  confined  to  the  equilibrium  and  mo- 
tion of  solids.  A  distinct  appellation  is  wanted  for  the  latter  branch  of  the  science. 
The  titla  STEREOS-FATICS  has  been  suggested 


172  A    TREATISE    ON    PNEUMATICS.  CHAP.    I. 

supposed  that  so  long  as  a  body  continues  to  receive  heat  from 
fire  applied  to  it,  or  from  any  other  source,  so  long  its  tempera- 
ture will  increase,  and  the  body  will  become  hotter.  That  this 
supposition  is  erroneous  is  easily  proved.  Let  a  quantity  of 
ice  at  the  temperature  of  32°  be  placed  in  a  vessel  containing 
six  times  its  quantity  of  water  at  the  boiling  heat.  The  water 
will  immediately  begin  to  lose  its  heat  by  imparting  it  to  the 
ice ;  but,  meanwhile,  the  temperature  of  the  ice  will  not  be 
increased.  After  the  lapse  of  a  sufficient  time,  the  whole  of 
the  ice  will  be  liquefied  and  intermixed  with  the  water ;  and 
it  will  be  found  that  the  entire  contents  of  the  vessel  in  the 
liquid  state  have  the  temperature  of  only  32°.  Now  here  it  is 
obvious  that  the  water  originally  contained  in  the  vessel  has 
lost  so  much  of  its  heat  as  to  be  reduced  to  the  temperature  of 
the  ice.  But,  on  the  other  hand,  the  ice  has  not  shown  an  in- 
creased effect  on  the  thermometer  or  on  the  senses,  notwith- 
standing the  large  quantity  of  heat  which  it  has  most  certainly 
imbibed.  The  developement  of  the  theory,  founded  upon  this 
remarkable  fact,  does  not  belong  to  the  department  of  physics 
with  which  we  are  at  present  engaged  ;  but  the  mere  statement 
of  the  fact  is  sufficient  to  prove  that  we  are  not  to  infer,  that 
because  steam,  and  the  water  from  which  it  has  been  raised, 
produce  the  same  effect  on  the  thermometer  or  the  senses,  they 
therefore  contain  the  same  quantity  of  heat,  and  that  the  fact 
of  one  body  being  hotter  or  colder  than  another  does  not  justify 
the  inference  that  the  one  contains  more  or  less  heat  than  the 
other. 

(123.)  As  an  elastic  fluid  has  the  property  of  dilating  itse]f 
when  the  limits  of  the  space  within  which  it  is  confined  are 
enlarged,  it  is  also  characterized  and  distinguished  from  solids 
and  liquids  by  its  power  of  yielding  to  any  force  exceeding  the 
energy  with  which  its  particles  repel  each  other,  and  tending 
to  contract  the  limits  of  the  space  within  which  it  is  enclosed.* 
This  quality  is  called  compressibility  ;  and  although  under  ex- 
treme circumstances  it  is  proved  by  experiment  to  exist  in  a 
slight  degree  in  liquids,  and,  probably,  is  a  quality  in  which  all 

*  Solids  and  liquids  appear  to  differ  from  aeriform  fluids,  in  the  vast  energy  with 
which  the  particles  of  a  solid  or  liquid  repel  each  other  when  made  to  approximate 
by  external  pressure.  Consequently  the  application  of  any  external  force  pro- 
duces but  a  slight  compression,  and  the  effect  of  a  moderate  compressing  force  is 
insensible.  On  the  other  hand,  when  the  particles  are  at  that  distance  at  which 
they  are  naturally  placed  by  their  molecular  forces,  any  separation  to  a  greater 
distance  is  opposed  by  their  cohesion,  a  property  which  is  not  possessed  by  aeri- 
form bodies,  and  is  therefore  another  characteristic  which  distinguishes  solids  and 
liquids  from  aeriform  fluids.  Hence  the  mere  removal  of  a  compressing  force  oc- 
casions no  dilatation  of  the  two  former  beyond  a  certain  bulk.  It  is  highly  proba- 
ble, that  solids  differ  from  liquids  in  possessing  a  certain  arrangement  of  their 
constituent  parts,  which  is  identical  with  crystallization  in  some  cases,  and  analo- 
gous to  it  in  all  others,  though  in  a  greater  or  less  degree  in  different  solids. — 
AM.  ED. 


CHAP.    I.  VAPOR.  173 

bodies  in  some  degree  participate  ;  yet  it  belongs  so  conspicu- 
ously to  bodies  in  the  gaseous  form,  that  they  are  frequently 
denominated  compressible  fluids •,  in  contradistinction  to  liquids, 
which  are  often  called  incompressible  fluids.  Upon  the  applica- 
tion of  great  force,  liquids  are  found  to  yield  in  a  very  small 
degree  in  their  dimensions ;  this  effect,  however,  is  so  slight, 
and  produced  under  such  extreme  circumstances,  that  it  is 
found  that  a  mechanical  theory  of  liquids,  proceeding  upon 
their  assumed  incompressibility,  gives  results  which  have  no 
variation  from  the  actual  phenomena  of  any  practical  impor- 
tance. Such,  however,  is  not  the  case  with  elastic  fluids ;  they 
yield  upon  the  application  of  inconsiderable  pressure  ;  and  they 
allow  their  dimensions  to  be  contracted  in  all  cases  to  a  very 
great  extent,  and  in  many  without  any  practical  limit.  The 
consequences  and  laws  of  compressibility  and  expansibility,  aa 
they  are  found  to  exist  in  elastic  fluids,  will  be  more  fully  no- 
ticed hereafter. 

(124.)  Of  the  various  elastic  fluids  which  are  observed  in 
nature,  some  have  never  been  found  in  the  liquid  form ;  and 
many  of  these  have  never  been  by  any  process  of  art  reduced 
to  that  form  ;  such,  for  example,  is  atmospheric  air :  bodies  of 
this  kind  are  called  permanently  elastic  fluids.  By  these  words, 
however,  the  impossibility  of  their  reduction  to  the  liquid  state 
is  not  intended  to  be  assumed  ;  it  is  only  intended  to  express 
the  fact,  that  such  reduction  has  not  been  made.  The  name 
"  gases"  is  also  commonly  applied  to  bodies  of  this  class.  When 
bodies  more  commonly  exist  in  the  liquid  state,  but  by  natural 
heat  and  other  causes  sometimes  receive  the  elastic  form,  the 
elastic  fluid  is  called  vapor  :*  thus,  for  example,  when  heat  is 
applied  to  quicksilver,  the  elastic  fluid  which  is  produced  is 
called  the  vapor  of  quicksilver,  and  the  process  is  called 
vaporization.  The  lighter  liquids,  such  as  sether,  are  converted 
into  vapor  by  the  common  temperature  of  the  atmosphere  ;  the 
vapor  of  water  is  catted  steam.  This  term  steam,  however,  is 
sometimes,  though  not  with  such  strict  propriety,  used  synony- 
mously with  the  word  vapor. 

(125.)  Those  mechanical  properties  of  elastic  fluids  which 
have  generally  been  assigned  to  PNEUMATICS  are  the  qualities 
which  are  found  in  atmospheric  air ;  many  of  these  qualities 
extend  without  modification  to  all  elastic  fluids  whatsoever ; 
but  there  are.  some  of  them  which,  especially  when  applied  to 

*  Any  aeriform  fluid  must  be  considered  either  as  a  gas  or  a  vapor.  Now,  as 
most  of  those  aeriform  fluids  which  have  been  hitherto  considered  as  gases,  have 
been  actually  reduced  to  the  liquid  state  by  great  pressure  and  intense  cold,  and 
even  by  pressure  alone,  and  as  these  arc  excluded  from  the  class  of  vapors  by  our 
author's  definition,  it  would  probably  be  better  to  define  gases  to  be,  those  aeri- 
form fluids  which  have  never  been  reduced  to  the  liquid  state  under  mere  atmoa 
pheric  pressure  at  any  natural  temperature. — An.  ED. 
15 


174  A    TREATISE    ON    PNEUMATICS.  CHAP.    II. 

vapor,  require  to  be  restricted  and  modified  by  various  circum- 
stances which  belong  rather  to  the  theory  of  heat  than  to  the 
subject  of  the  present  treatise.  There  are  also  many  circum- 
stances to  be  attended  to  in  explaining-  the  properties  of  various 
gases,  which  belong  to  those  departments  of  physics  in  which 
the  production  and  constitution  of  these  gases  are  explained. 
The  province  of  PNEUMATICS  may,  therefore,  be  considered  as 
chiefly  and  immediately  confined  to  the  investigation  of  the 
mechanical  properties  of  the  atmosphere  ;  it  being  at  the  same 
time  understood  that  the  various  theorems  which  shall  be  es- 
tablished are  to  be  carried  into  other  departments  of  physics, 
there  to  undergo  such  restrictions  and  modifications  as  will  ren- 
der them  applicable  to  vapors  and  the  various  species  of  gases. 


CHAP.  II. 

PROPERTIES  OF  ATMOSPHERIC'AIR. 

AT3IOSPHERIC  AIR  IS  MATERIAL. — ITS  COLOR. — CAUSE  OF  THE  TLUE 
SKY. — CAUSE  OF  THE  GREEN  SEA. — AIR  HAS  WEIGHT. — EXPERI- 
MENTAL PROOFS. — AIR  HAS  INERTIA. — EXAMPLES  OF  ITS  RESIST- 
ANCE.— IT  ACQUIRES  MOVING  FORCE. — EXAMPLES  OF  ITS  IMPACT. 
— AIR  IS  IMPENETRABLE. — EXPERIMENTAL  PROOFS. 

(126.)  THE  atmosphere  is  the  thin  transparent  fluid  which 
surrounds  the  earth  to  a  considerable  height  above  its  surface, 
and  which,  in  virtue  of  one  of  its  constituent  elements,  sup- 
ports animal  life  by  respiration,  and  is  necessary  also  to  the 
due  exercise  of  the  vegetable  functions.  This  substance  is 
generally,  but  erroneously,  regarded  as  invisible.  That  it  is 
not  invisible  may  be  proved  by  turning  our  view  to  the  firma- 
ment :  that,  in  the  presence  of  light,  Appears  a  vault  of  an 
azure  or  blue  color.  This  color  belongs  not  to  any  thing  which 
occupies  the  space  in  which  the  stars  and  other  celestial  objects 
are  placed,  but  to  the  mass  of  air  through  which  these  bodies 
are  seen.  It  may  probably  be  asked,  If  the  air  be  an  azure- 
colored  body,  why  is  not  that  which  immediately  surrounds  us 
perceived  to  have  this  azure  color,  in  the  same  manner  as  a  blue 
liquid  contained  in  a  bottle  exhibits  its  proper  hue-?  The  ques- 
tion is  easily  answered. 

There  are  certain  bodies  which  reflect  color  so  faintly,  that 
when  they  exist  in  limited  quantities,  the  portion  of  colored 
light  which  they  transmit  to  the  eye  is  insufficient  to  produce 
sensation,  that  is,  to  excite  in  the  mind  a  perception  of  the  color. 
Almost  all  semi-transDarent  bodies  are  examples  of  this. 


CHAP.    II.  COLOR    OF    AIR.  175 

Let  a  champagne  glass  be  filled  with  sherry,  or  other  wine  of 
that  color ;  at  the  thickest  part,  near  the  top  of  the  glass,  the 
wine  will  strongly  exhibit  its  peculiar  color^but  as  the  glass 
tapers,  and  its  thickness  is  diminished,  this  color  will  become 
more  faint ;  and  at  the  lowest  point,  it  will  almost  disappear, 
the  liquid  seeming  nearly  as  transparent  as  water. 

Now  let  a  glass  tube,  of  very  small  bore,  be  dipped  in  the 
same  wine,  and,  the  finger  being  applied  to  the  upper  end,  let 
it  be  raised  from  the  liquid ;  the  wine  will  remain  suspended  in 
the  tube ;  and  if  it  be  looked  at  through  the  tube  it  will  be 
found  to  have  all  the  appearance  of  water,  and  to  be  colorless. 
In  this  case  there  can  be  no  doubt  that  the  wine  in  the  tube 
has  actually  the  same_color  as  the  liquid  of  which  it  originally 
formed  a  part,  but  existing  only  in  a  small  quantity,  that  color 
is  transmitted  to  the  eye  so  faintly  as  to  be  inefficient  in  pro- 
ducing perception. 

The  water  of  the  sea  exhibits  another  remarkable  example 
of  this  effect.  If  we  look  into  the  sea  where  the  water  has 
considerable  depth,  we  find  that  its  color  is  a  peculiar  shade  of 
green ;  but  if  we  take  up  a  glass  of  the  water  which  thus  ap- 
pears green,  we  shall  find  it  perfectly  limpid  and  colorless. 
The  reason  is,  that  the  quantity  contained  in  the  glass  reflects 
to  the  eye  too  small  a  quantity  of  the  color  to  be  perceivable  ; 
while  the  great  mass  of  water,  viewed  when  we  look  into  the 
deep  sea,  throws  up  the  color  in  such  abundance  as  to  produce 
a  strong  and  decided  perception  of  it. 

The  atmosphere  is  in  the  same  circumstances  :  the  color 
from  even  a  considerable  portion  of  it  is  too  faint  to  be  percep- 
tible. Hence  the  air  which  fills  an  apartment,  or  which  im- 
mediately surrounds  us  when  abroad,  appeal's  colorless  and 
perfectly  transparent.  But  when  we  behold  the  immense  mass 
of  atmosphere  through  which  we  view  the  firmament,  the  color 
is  reflected  with  sufficient  force  to  produce  distinct  perception. 
But  it  is  not  necessary  for  this  that  so  great  an  extent  of  air 
should  be  exhibited  to  us  as  that  which  farms  the  whole  depth 
or  thickness  of  the  atmosphere.  Distant  mountains  appear 
blue,  not  because  that  is  their  color,  but  because  it  is  the  color 
of  the  medium  through  which  they  are  seen. 

Although  the  preceding  observations  belong  more  properly 
to  optics  than  to  our  present  subject ;  yet  still,  since  the  ex- 
hibition of  color  is  one  of  the  manifestations  of  the  presence  of 
body,  they  may  not  be  considered  as  foreign  to  an  investiga- 
tion of  the  mechanical  properties  of  atmospheric  air.  The  mind 
unaccustomed  to  physical  inquiries  finds  it  difficult  to  admit 
that  a  thing  so  light,  attenuated,  impalpable,  and  cpparently 
spiritual,  should  be  composed  of  parts  whose  leading  properties 
are  identical  with  those  of  the  most  solid  and  adamsntii  e  masses 


176  A    TREATISE    ON    PNEUMATICS.  CHAP.    II. 

The  knowledge  that  we  see  the  air  must  at  least  prepare 
the  mind  for  the  admission  of  the  truth  of  the  proposition  that 
air  is  a  body.  .  • 

(127.)  Among  the  properties  which  are  observed  to  appertain 
to  matter,  and  which,  as  far  as  we  know,  are  inseparable  from 
it,  in  whatever  form,  and  under  whatever  circumstances  it  ex- 
ists, weight  and  inertia  hold  a  conspicuous  place.  To  be  con- 
vinced, therefore,  that  air  is  material,  we  ought  to  ascertain 
whether  it  possesses  these  properties.  In  the  subsequent  parts 
of  the  present  treatise,  we  shall  have  numerous  proofs  of  this  ; 
but  it  will  at  present  be  convenient  to  demonstrate  it  in  such  a 
manner  that  we  shall  be  warranted  in  assuming  it,  in  some  of 
the  explanations  which  we  shall  have  to  offer. 

(128.)  The  most  direct  proof  that  air  has  weight  is  the  fact, 
that  if  a  quantity  of  it  be  suspended  from  one  arm  of  a  balance, 
it  will  require  an  absolute  weight  to  counterpoise  it  in  the  op- 
posite scale.  By  the  aid  of  certain  pneumatical  engines,  the 
nature  of  which  will  be  explained  hereafter,  but  the  operation 
and  eifects  of  which  will  for  the  present  be  assumed,  this  may 
be  experimentally  established. 

Let  a  vessel,  containing  aboui  two  quarts,  be  formed  of  thin 
copper,  with  a  narrow  neck,  in  which  is  placed  a  stopcock,  by 
turning  which,  the  vessel  may  be  opened  or  closed  at  pleasure. 
Let  two  instruments  be  provided  called  syringes,  one  the  ex- 
hausting syringe,  and  the  other  the  condensing  syringe.  The 
nature  of  these  instruments  will  be  hereafter  explained.  Let 
the  exhausting  syringe  be  screwed  upon  the  neck  of  the  vessel, 
and  let  the  stopcock  be  opened,  so  that  the  interior  of  the  ves- 
sel shall  have  free  communication  with  the  bottom  of  the 
syringe  ;  if  the  syringe  be  now  worked,  a  large  portion  of  the 
air  contained  in  the  vessel  may  be  withdrawn  from  it.  When 
this  has  been  done,  let  the  stopcock  be  closed  to  prevent  the 
admission  of  air,  and  let  the  vessel  be  detached  from  the  syr- 
inge. Let  it  then  be  placed  in  the  dish  of  a  well  constructed 
balance,  and  accurately  counterpoised  by  weights  in  the  oppo- 
site scale.  The  weight  which  is  thus  counterpoised  is  that  of 
the  vessel,  and  the  small  portion  of  air  which  remains  in  it,  if 
the  latter  have  any  weight.  Let  the  stopcock  be  now  opened, 
and  the  external  air  will  be  immediately  heard  rushing  into  the 
vessel.  When  a  small  quantity  has  been  thus  admitted,  let  the 
stopcock  be  again  closed.  It  will  be  found  that  the  copper 
vessel  is  now  heavier,  in  a  small  degree,  than  it  was  before  the 
air  was  admitted,  for  the  arm  of  the  balance  from  which  it  is 
suspended  will  be  observed  to  preponderate.  Let  such  addi- 
tional weights  be  placed  in  the  opposite  scale  as  will  restore 
equilibrium.  The  stopcock  being  now  once  more  opened,  the 
air  will  be  observed  to  rush  in  as  before,  and  will  continue  to 


CHAP.    II.  INERTIA    OP    AIR.  177 

do  so  until  as  much  has  passed  into  the  vessel  as  it  contained 
before  the  exhausting  syringe  was  applied.  The  weight  of  the 
vessel  will  now  be  observed  to  be  further  increased,  the  end  of 
the  beam  from  which  it  is  suspended  preponderating. 

These  facts  are  perhaps  sufficient  proofs  that  air  has 
weight :  but  the  experiment  may  be  carried  further.  Let  the 
condensing  syringe  be  now  attached  to  the  neck  of  the  vessel, 
and  let  the  stopcock  in  the  neck  be  opened  so  as  to  leave  a  free 
communication  between  the  vessel  and  the  bottom  of  the  syr- 
inge. The  construction  of  this  instrument,  which  will  be  ex- 
plained hereafter,  is  such,  that  by  working  it,  an  increased 
quantity  of  air  may  be  forced  into  the  vessel  to  any  extent 
which  the  strength  of  tho  vessel  is  capable  of  bearing.  A  con- 
siderably increased  quantity  of  air  being  thus  deposited  in  the 
vessel,  let  the  stopcock  be  closed  so  as  to  prevent  its  escape. 
The  vessel,  being  detached  from  the  syringe,  is  restored  to  the 
dish  of  the  balance  ;  the  weights  which  counterpoised  it  before 
the  increased  quantity  of  air  was  forced  in  still  remaining  un- 
changed in  the  opposite  scale.  The  vessel  will  now  no  longer 
remain  counterpoised,  but  will  preponderate,  and  will  require 
an  increased  weight  in  the  opposite  scale  to  restore  it  to  equi- 
librium. 

In  this  experiment  we  see  that  every  increase  which  is  given 
to  the  quantity  of  air  contained  in  a  vessel  produces  a  corres- 
ponding increase  in  its  weight,  and  that  every  diminution  of 
the  quantity  of  air  it  contains  produces  a  corresponding  diminu- 
tion in  its  weight.  Hence  we  infer,  that  the  air  which  is  in- 
troduced into  or  withdrawn  from  the  vessel  has  weight,  and  that 
it  is  by  the  amount  of  its  weight  that  the  weight  of  the  vessel  is 
increased  or  diminished. 

We  shall  hereafter  have  many  other  instances  of  the  gravita- 
tion of  atmospheric  air ;  but  we  shall,  for  the  present,  assume 
the  principle  that  air  has  weight,  founded  on  the  experimental 
proof  just  given. 

(129.)  That  air  in  common  with  all  other  bodies  possesses  the 
quality  of  inertia,  numerous  familiar  effects  make  manifest. 
Among  the  effects  which  betray  this  quality  in  solid  bodies,  is 
the  fact  th*t,  when  one  solid  body  puts  another  in  motion,  the 
former  loses  as  much  force  as  the  latter  receives.  This  loss  of 
force  is  called  resistance,  and  is  attributed  to  the  quality  of 
inertia,  or  inability  in  either  the  striking  or  struck  body  to  call 
into  existence  more  force  in  a  given  direction  than  previously 
existed.  When  the  atmosphere  is  calm  and  free  from  Avind,  the 
particles  of  air  maintain  their  position,  and  are  in  a  state  of  rest. 
If  a  solid  body,  presenting  a  broad  surface,  be  moved  through 
the  air  in  this  state,  it  must,  as  it  moves,  drive  before  it  and  put 
in  motion  those  parts  of  the  air  which  lie  in  the  space  through 


178  A    TREATISE    ON    PNEUMATICS.  CHAP.    II. 

which  it  passes.  Now  if  the  air  had  no  inertia,  it  would  require 
no  force  to  impart  this  motion  to  them,  and  to  drive  them  before 
the  moving  solid  ;  and  as  no  force  would  in  that  case  be  im- 
parted to  the  air,  so  no  force  would  be  lost  by  the  solid :  in 
other  words,  the  solid  would  suffer  no  resistance  to  its  motion. 

But  every  one's  experience  proves  this  not  to  be  the  case. 
Open  an  umbrella,  and  attempt  to  carry  it  along  swiftly  with 
its  concave  side  presented  forwards  ;  it  will  immediately  be 
felt  to  be  opposed  by  a  very  considerable  resistance,  and  to  re- 
quire a  great  force  to  draw  it  along.  Yet  this  force  is  nothing 
more  than  what  is  necessary  to  push  the  air  before  the  um- 
brella. 

On  the  deck  of  a  steam-boat,  propelled  with  any  considera- 
ble speed,  we  feel  on  the  calmest  day  a  breeze  directed  from 
the  stem  to  the  stern.  This  arises  from  the  sensation  produced 
by  our  body  displacing  the  air  as  we  are  carried  through  it. 

It  is  the  inertia  of  the  atmosphere  which  gives  effect  to  the 
wings  of  birds.  Were  it  possible  for  a  bird  to  live  without 
respiration,  and  in  a  space  void  of  air,  it  would  tfo  longer  have 
the  power  of  flight.  The  plumage  of  the  wings  being  spread, 
and  acting  with  a  broad  surface  on  the  atmosphere  beneatli 
them,  is  resisted  by  the  inertia  of  the  atmosphere,  so  that  the 
air  forms  a  fulcrum,  as  it  were,  on  which  the  bird  rises  by  the 
leverage  of  its  wings. 

As  a  body  at  rest  manifests  its  inertia  by  the  resistance  which 
it  offers  when  put  in  motion,  so  a  body  in  motion  exhibits  the 
same  quality  by  the  force  with  which  it  strikes  a  body  at  rest. 
We  have  seen  examples  of  the  resistance  which  the  atmosphere 
at  rest  offers  to  a  body  in  motion ;  but  the  force  with  which  the 
atmosphere  in  motion  acts  upon  a  body  at  rest  is  exhibited  by 
examples  far  more  numerous  and  striking.  Wind  is  nothing 
more  than  moving  air,  and  its  force,  like  that  of  every  other 
body,  depends  on  the  quantity  moved  and  the  speed  of  the  mo- 
tion. Every  example,  therefore,  of  the  effects  of  the  power  of 
wind  is  an  example  of  the  inertia  of  atmospheric  air.  In  a 
windmill,  the  moving  force  of  all  the  heavy  parts  of  the  ma- 
chinery is  derived  from  the  moving  force  of  the  wind  acting 
upon  the  sails,  and  the  resistance  of  the  work  to  wWch  the  mill 
is  applied  is  overcome  by  the  same  power.  A  ship  is  propelled 
through  the  deep,  and  the  deep  itself  is  agitated  and  raised  in 
waves,  by  the  inertia  of  the  atmosphere  in  motion.  As  the  ve- 
locity increases,  the  for^  becomes  more  irresistible ;  and  we 
find  buildings  totter,  trees  torn  from  the  roots,  and  even  the 
solid  earth  itself  yield  before  the  force  of  the  hurricane. 

(130.)  Since  air  may  be  seen  and  felt,  since  it  has  color  and 
weight,  and  since  it  opposes  resistance  when  acted  upon,  and 
strikes  with  a  force  proportionate  to  the  speed  of  its  motion, 


CHAP.    II. 


IMPENETRABILITY    DF    AIR. 


179 


we  can  scarcely  hesitate  to  admit  that  it  has  qualities  which 
entitle  it  to  be  classed  among  material  substances  :  but  one 
other  quality  still  remains  to  be  noticed,  which,  perhaps,  decides 
its  title  to  materiality  more  unanswerably  than  any  of  the  oth- 
ers. Air  is  impenetrable  ;  it  enjoys  that  peculiar  property  of 
matter,  by  which  it  refuses  admission  to  any  other  body  to  the 
space  it  occupies,  until  it  quit  that  space.  This  property  air 
possesses  as  positively  as  adamant.  The  difficulty  which  is 
commonly  felt  in  conceiving  the  impenetrability  of  substances 
of  this  nature,  arises  partly  from  confounding  the  quality  of  im- 
penetrability with  that  of  hardness,  and  partly  from  not  attend- 
ing to  the  fact  that,  when  a  body  moves  through  the  air,  it 
drives  the  air  before  it  in  the  same  manner  as  a  vessel  moving 
through  the  water  propels  that  fluid. 

Let  a  bladder  be  filled  with  air,  and  tied  at  the  mouth ;  we 
shall  then  be  able  to  feel  the  air  it  contains  as  distinctly  as  if 
the  bladder  were  filled  with  a  solid  body.  We  shall  find  it  im- 
possible, so  long  as  the  air  is  prevented  from  escaping,  to  press 
the  sides  of  the  bladder  together;  and  if  the  bladder  be  sub- 
mitted to  such  severe  pressure  as  may  be  produced  by  mechan- 
ical means,  it  will  burst  before  the  air  will  allow  it  to  collapse. 

That  air  will  not  allow  the  entrance  of  another  body  into  the 
space  where  it  is  present,  may  also  be  proved  by  the  following 
experiment. 

Let  A  B,  Jig.  3.,  be  a  glass  vessel  open  at  the  end  A,  and 
having  a  short  tube  from  the  bottom,  furnished  with  a  stopcock 
C.  Let  D  E,  Jig.  4.,  be  another  glass  vessel  containing  water. 


Fig,  3. 


Fig.  4. 


Fig.  5. 


On  the  surface  of  this  water  let  a  small  piece  of  cork  F  float. 
Let  the  vessel  A  B,  having  the  stopcock  C  closed,  be  now  in- 
verted ;  let  its  mouth  A  be  placed  over  the  cork  F,  and  let  it 
thus  be  pressed  to  any  depth  in  the  reservoir  D  E.  If  the  air 
in  A  B  were  capable  of  permitting  the  entrance  of  another  body 
into  the  space  in  which  it  is  present,  the  water  in  the  reservoir 


180  A    TREATISE    ON    PNEUMATICS.  CHAP.    II. 

I)  E  would  now  enter  at  the  mouth  of  the  vessel  A,  and  rising 
in  it  would  stand  at  the  same  level  within  the  vessel  A  B  as 
that  which  it  has  without  it.  But  this  is  not  found  to  be  the 
case.  When  the  vessel  A  B  is  pressed  into  the  reservoir,  the 
surface  of  the  water  within  A  B  will  be  observed  still  near  the 
mouth  A,  as  will  be  indicated  by  the  position  of  the  cork  which 
floats  upon  it,  and  as  is  represented  in  Jig.  5.  It  appears, 
therefore,  manifestly,  that,  whatever  be  the  cause,  the  water  is 
excluded  from  the  vessel  A  B.  That  this  cause  is  the  presence 
of  the  air  included  in  the  vessel  is  proved  by  opening  the  stop- 
cock C,  and  allowing  the  air  to  escape.  By  the  established 
principles  of  hydrostatics,  the  surface  of  the  water  within  the 
vessel  A  B  exerts  an  upward  pressure  proportionate  to  the 
depth  of  that  surface  below  the  surface  of  the  water  exterior  to 
the  vessel  A  B.  This  pressure,  acting  upon  the  air  enclosed  in 
the  vessel  A  B,  forces  it  out  the  moment  the  stopcock  C  is 
opened,  and  immediately  the  surface  of  the  water  within  A  B 
rises  to  the  level  of  the  surface  without  it. 

We  have  stated  that  the  surface  of  the  water  within  A  B  re- 
mains nearly  at  the  mouth  of  that  vessel  when  it  is  plunged  in 
the  reservoir.  It  would  remain  exactly  at  the  mouth,  if  air  were 
incompressible  ;  but,  on  the  contrary,  this  fluid  is  highly  com- 
pressible, allowing  itself  to  be  forced  into  reduced  dimensions 
l>y  the  application  of  adequate  mechanical  force.  It  is  neces- 
?  sary,  however,  nbt  to  confound  compressibility  with  penetrabil- 
ity. So  far  from  these  qualities  being  identical,  the  one 
implies  the  absence  of  the  other.  A  body  is  compressible 
when  the  forcible  intrusion  of  another  body  into  the  space  with- 
in which  it  is  confined  causes  its  particles  to  retreat,  and  to 
accommodate  their  arrangement  to  the  more  limited  space 
within  which  they  are  compelled  to  exist.  The  very  fact  of 
their  thus  retreating  before  the  intruding  body  is  a  distinct 
manifestation  of  their  impenetrability.  If  they  were  penetra- 
ble, the  body  would  enter  the  space  in  which  they  were  confined, 
without  driving  them  before  it,  or  otherwise  disturbing  their 
arrangement. 


CHAP.    III. 


ELASTICITY    OF    AIR. 


181 


CHAP.  III. 

ELASTICITY  OF  AIR. 

ELASTIC  AND  COMPRESSING  FORCES  EQUAL. — LIMITED  HEIGHT  OF 
THE  ATMOSPHERE. — ELASTICITY  PROPORTIONAL  TO  THE  DENSITY. 
— EXPERIMENTAL  PROOFS. — INTERNAL  AND  EXTERNAL  PRESSURE 
ON  CLOSE  VESSELS  CONTAINING  AIR. 

(131.)  THE  elasticity  and  compressibility  of  air  have  been 
already  noticed.  In  the  present  chapter  we  propose  to  exam- 
ine and  explain  these  qualities  in  more  detail. 

It  will  be  evident,  upon  the  slightest  reflection,  that  the  elas- 
ticity of  air  must  be  equal  to  the  force  which  is  necessary 
to  confine  it  within  the  space  it  occupies.  Let  us  suppose  that 
A  B,  Jig.  6.,  is  a  cylinder,  having  a  piston  P  fitting  air-tight  at 

Fig.  G. 


the  top  ;  and  let  us  imagine  that  this  piston  P  is  not  acted  upon 
by  any  external  force,  having  a  tendency  to  keep  it  in  its  place. 
If  the  cylinder  below  the  piston  be  filled  with  air,  this  air  will 
have  a  tendency,  by  virtue  of  its  elasticity,  to  expand  into  a 
wider  space  ;  and  this  tendency  will  be  manifested  by  a  pres- 
sure exerted  by  the  air  on  all  parts  of  the  surfaces  which  con- 
fine it.  The  piston  P  will,  therefore,  be  subject  to  a  force 
tending  to  displace  it  and  drive  it  from  the  cylinder,  the  amount 
of  which  will  be  the  measure  of  the  elasticity  of  the  air  beneath 
it.  Now,  if  this  piston  be  not  subject  to  the  action  of  a  force 
directed  inwards,  exactly  equal  in  amount  to  the  pressure  thus 
excited  by  the  elastic  force  of  the  air,  it  cannot  maintain  its  po- 
sition. If  it  be  subject  to  an  inward  force  of  less  amount  than 
the  elastic  pressure,  then  the  latter  will  prevail,  and  the  piston 
be  forced  out.  If  it  be  subject  to  an  inward  force  greater  in 
16 


182  A    TREATISE    ON    PNEUMATICS.  CHAP.   III. 

amount  than  the  elastic  pressure,  then  the  former  will  prevail, 
and  the  piston  will  be  forced  in,  the  air  being  compelled  to  re- 
treat within  a  more  confined  space.  In  no  case,  therefore,  can 
the  piston  maintain  its  position,  except  when  it  is  subject  to  an 
inward  pressure  exactly  equal  to  the  elastic  force  of  the  ai*  en- 
closed in  the  cylinder. 

The  property  of  elasticity  renders  it  necessary  that,  in  what- 
ever state  air  exist,  it  shall  be  restrained  by  adequate  forces  of 
some  definite  amount,  and  which  serve  as  antagonist  principles 
to  the  unlimited  power  of  dilatation  which  the  elastic  property 
implies.  In  all  cases  which  fall  under  common  observation, 
air  is  either  restrained  by  the  resistance  of  solid  surfaces,  or  it 
is  pressed  by  the  incumbent  weight  of  the  mass  of  atmosphere 
placed  above  it.  It  may  be  asked,  however,  whether  it  will  not 
follow  from  this,  that  the  extent  of  our  atmosphere  is  infinite  ? 
for  that,  as  we  ascend  in  it,  the  weight  of  the  superior  mass  of 
air  must  be  gradually  and  unceasingly  lessened ;  and,  therefore, 
the  force  which  resists  the  expansive  principle  being  removed 
by  degrees,  the  fluid  will  spread  through  dimensions  which  are 
subject  to  no  limitation.  Although  it  is  undoubtedly  true  that 
these  considerations  lead  us  justly  to  conclude  that  our  atmos- 
phere extends  to  a  very  great  distance  from  the  surface,  and 
that  the  higher  strata  of  it  are  attenuated  to  a  degree  which 
not  only  exceeds  the  powers  of  art  to  imitate,  but  even  out- 
strips the  powers  of  imagination  to  conceive  ;  yet  still  the  un- 
derstanding can  suggest  a  definite  limit  to  this  expansion. 
Numerous  physical  analogies*  favor  the  conclusion,  that  the 
divisibility  of  matter  has  a  limit,  or  that  all  material  substances 
consist  of  ultimate  constituent  particles  or  atoms,  which  admit 
of  no  further  subdivision,  and  on  the  mutual  relations  of  which 
the  form  and  properties  of  the  various  species  of  bodies  depend. 

Now,  those  ultimate  particles  of  the  air  are  endued  with  a 
certain  definite  weight,  because  it  is  the  aggregate  of  their 
weights  which  forms  the  weight  of  any  mass  of  air.  It  is  a  fact 
established  by  experiment,  that  in  proportion  as  air  expands, 
its  elastic  force  is  diminished  ;  and,  therefore,  if  it  continue  to 
expand,  it  will  at  length  attain  a  state  of  attenuation  in  which 
the  disposition  of  its  constituent  particles  to  separate  by  their 
elasticity  is  so  far  diminished,  as  not  to  exceed  the  gravity  of 
those  constituent  particles  themselves.  In  this  state  the  two 
forces  will  be  in  equilibrium,  and  the  elastic  force  being  neu- 
tralized, the  particles  will  no  longer  be  dilated. 

(132.)  In  these  observations  we  have  assumed  a  principle 
which  is  of  the  last  importance  in  pneumatics,  and  which,  in- 
deed, may  be  regarded  as  forming  the  basis  of  this  part  of 

*  Cab.  Cyc.  Mechanics,  chap.  ii. 


CHAP.    III. 


LIMITS    OF    THE    ATMOSPHERE. 


183 


physical  science,  in  the  same  manner  as  the  power  of  transmit- 
ting pressure  is  the  fundamental  principle  of  hydrostatics. 
This  latter  principle,  indeed,  also  extends  to  elastic  fluids ;  and 
all  the  consequences  of  the  free  transmission  of  pressure,  which 
do  not  also  involve  the  supposition  of  incompressibility,  are  ap- 
plicable to  elastic  fluids  with  as  much  truth  as  to  liquids.  But 
the  principle  to  which  we  now  more  especially  refer,  and  which 
may  be  looked  upon  as  the  chief  characteristic  of  this  form  of 
body,  and  necessary  to  render  definite  the  notion  of  their  elas- 
ticity, may  be  announced  as  follows  : — 

"  The  elastic  force  of  any  given  portion  of  air  is  augmented 
in  exactly  the  same  proportion  as  the  space  within  which  it  is 
enclosed  is  diminished ;  and  its  elastic  force  is  diminished  in 
exactly  the  same  proportion  as  the  space  through  which  it  is 
allowed  to  expand  is  augmented." 

To  explain  this,  let  A  B  C  D,  Jig.  7.,  be  conceived  to  be  a 


B 


cylinder,  in  which  a  piston  A  B  moves  air-tight  and  without 
friction ;  and  let  us  suppose  the  distance  of  the  lower  surface 
A  B  of  the  piston  from  the  bottom  D  C  of  the  cylinder  to  be  13 
inches.  Let  air  be  imagined  to  be  enclosed  below  the  pis- 
ton, and  let  us  suppose  that  the  elastic  force  of  this  air  is  such 
as"  to  press  the  piston  with  a  force  of  16  ounces.  From  what 
'has  been  already  stated  (131.),  it  is  clear  that  to  maintain  the 
piston  in  its  place,  it  is  necessary  that  it  should  be  pressed 
downwards  with  an  equivalent  force  of  16  ounc*es.  Now  let 
the  force  upon  the  piston  be  doubled,  or  let  the  piston  be  loaded 
with  a  pressure  of  32  ounces.  The  inward  pressure  prevailing 
over  the  elasticity,  the  piston  will  immediately  be  forced  to- 
wards D  C,  but  will  cease  to  move  at  a  certain  distance  A  D, 
Jig.  8.,  from  the  bottom.  Now,  if  this  distance  A  D  be  meas- 
ured, it  will  be  found  to  be  exactly  six  inches.  The  air  has, 
therefore,  contracted  itself  into  half  its  former  dimensions. 
Since  the  piston  is  sustained  in  the  position  represented  in 


184 


A    TREATISE    ON    PNEUMATICS. 


CHAP.    III. 


Jig.  8.,  it  follows  that  the  elasticity  of  the  air  beneath  it  is 
equivalent  to  the  weight  of  the  piston  A  B  ;  and,  therefore, 
that  the  air  included  in  the  cylinder  acquires  double  its  original 
elasticity  when  it  is  compressed  into  half  its  or/  'inal  bulk. 

Fig.  B. 


Let  the  piston  be  now  loaded  with  three  times  its  original 
weight,  or  48  ounces ;  it  will  be  observed  to  descend  into  the 
cylinder,  and  further  to  compress  the  air,  until  its  distance  from 
the  bottom  is  reduced  to  four  inches.  At  that  distance  it  will 
rest,  being  balanced  by  the  increased  elasticity  of  the  air:  this 
air  is  now  compressed  into  one  third  of  its  original  bulk,  and  it 
has  three  times  its  original  elastic  force. 

In  the  same  manner,  in  whatever  proportion  the  weight  of 
the  piston  be  augmented,  in  the  same  proportion  will  the  dis- 
tance from  the  bottom  at  which  it  will  rest  in  equilibrium  be 
diminished  ;  and,  consequently,  the  elastic  force  of  the  air  is 
increased  in  the  same  proportion  as  the  space  into  which  it  is 
compressed  is  diminished. 

Let  us  again  suppose  the  piston  to  be  loaded  with  sixteen 
ounces,  and  to  be  balanced,  as  in  Jig.  7.,  by  the  resistance  of 
the  air  at  twelve  inches  from  the  bottom  of  "the  cylinder.  But 
let  us  also  suppose  the  cylinder  continued  upwards  to  a  height 
exceeding  24  inches ;  let  the  weight  upon  the  piston  be  now 
reduced  to  eight  ounces.  Since  the  elasticity  of  the  air  be- 
neath the  piston  was  capable  of  supporting  sixteen  ounces,  it 
will  now  prevail  against  the  diminished  pressure  of  eight 
ounces.  The  piston  will  continue  to  rise  in  the  cylinder  until 
the  elasticity  of  the  air  is  so  far  diminished  by  expansion,  that 
it  is  capable  of  supporting  no  more  than  eight  ounces  ;  the  pis- 
ton will  then  remain  in  equilibrium.  If  the  height  of  the  piston 
above  the  bottom  be  now  measured,  it  will  be  found  to  be  24 
inches,  that  is,  double  its  former  height ;  the  air  has,  therefore, 
expanded  to  double  its  former  dimensions,  and  is  reduced  to 
half  its  former  elasticity. 


CHAP.    III. 


ELASTICITY    AS    THE    DENSITY. 


185 


Fig.  9. 


In  like  manner  it  may  be  shown,  that,  if  the  weight  upon  the 
piston  were  reduced  to  four  ounces,  or  a  fourth  of  its  original 
amount,  the  piston  would  rise  to  four  times  its  original  height, 
or  48  inches,  before  it  would  be  capable  of  balancing  the  re- 
duced elasticity  of  the  air.  Thus,  by  expanding  to  four  times 
its  primitive  dimensions,  the  elasticity  of  the  air  is  reduced  to 
one  fourth  of  its  primitive  amount. 

By  like  experiments,  it  is  easy  to  see  how  the  general  law 
may  be  established.  In  whatever  proportion  the  weight  of  the 
piston  may  be  increased  or  diminished,  in  the  same  proportion 
exactly  will  the  space  filled  by  the  air  which  balances  it  be  di- 
minished or  increased. 

(133.)  The  preceding  illustration  has  been  selected  with  a 
view  rather  to  make  the  property  itself  intelligible,  than  as  a 
practical  experimental  proof  of  it.  The  use  of  pistons  movable 
in  cylinders  is  attended  with  inconvenience  in  cases  of  this 
kind,  arising  from  the  effects  of  friction,  and  the  difficulties  of 
making  due  allowance  for  them.  There  is,  however,  another 
method  of  bringing  the  law  to  the  test  of  experiment,  which  is 
not  less  direct,  and  is  more  satisfactory. 

Let  ABC  D,Jig.  9.,  be  a  glass  tube  curv 
ed  at  one  end,  B  C,  and  having  the  short  leg 
C  D  furnished  with  a  stopcock  at  its  extrem- 
ity :  let  the  leg  B  A  be  more  than  60  inches 
in  length.  The  stopcock  D  being  opened  so 
as  to  allow  a  free  communication  with  the 
air,  and  the  mouth  A  of  the  longer  leg  being 
also  open,  let  as  much  mercury  be  poured 
into  the  tube  as  will  fill  the  curved  part  B  C, 
and  rise  to  a  small  height  in  each  leg.  By 
the  principles  of  hydrostatics,  the  surfaces 
of  the  mercury  E  and  F  will  stand  at  the 
same  level.  Let  the  stopcock  D  be  now 
closed,  the  levels  E  F  will  still  remain 
undisturbed.  When  the  stopcock  D  was 
opened,  the  surface  F  sustained  a  pressure 
equal  to  the  weight  of  a  column  of  air  con- 
tinued from  F  upwards  as  far  as  the  atmos- 
phere extends.  But  the  stopcock  D  being 
closed,  the  effect  of  the  weight  of  all  the 
air  above  that  point  is  intercepted  ;  and,  con- 
sequently, the  surface  F  can  sustain  no 
pressure  arising  from  weight,  except  the 
amount  of  the  weight  of  the  small  quantity  of  air  included  be- 
tween F  and  D,  which  is  altogether  insignificant.  But  the  air 
thus  included  presses  on  the  surface  F  by  its  elasticity ;  and 
the  amount  of  this  pressure  is  equal  to  the  force  which  confined 


186 


A    TREATISE    ON    PNEUMATICS. 


CHAP.    III. 


the  air  within  the  space  F  D,  before  the  stopcock  was  closed 
(131.) :  but  this  force  was  the  weight  of  the  column  of  atmos- 
phere above  D  ;  and  hence  it  appears,  that  the  elastic  force  of 
'the  air  confined  in  the  space  D  F  is  equal  to  the  atmospheric 
pressure. 

Now  the  other  surface  E,  the  end  A  of  the  tube  being  open, 
is  subject  to  the  atmospheric  pressure.  Thus  the  two  surfaces, 
F  and  E,  of  the  mercury,  are  each  subject  to  a  pressure  arising 
from  a  different  quality  of  the  atmosphere  ;  the  one,  F,  being 
pressed  by  its  elasticity,  and  the  other,  E,  being  pressed  by  its 
weight.  These  pressures  being  equal,  the  surfaces  F  and  "E 
continue  at  the  same  level. 

The  method  of  ascertaining,  experimentally,  the  pressure 
arising  from  the  weight  of  the  atmosphere  will  be  fully  explain- 
ed hereafter ;  meanwhile,  it  is  necessary  for  our  present  pur- 
pose to  assume  this  pressure  as  known.  Let  us  suppose,  then, 
that  the  atmospheric  pressure  acting  upon  the  surface  E  is  the 
same  as  would  be  produced  by  a  column  of  mercury  30  inches 
in  height  resting  on  the  surface  E :  the  force  with  which  the 
elasticity  of  the  air  confined  in  D  F  presses  on  the  surface  Fis 
therefore  equal  to  the  weight  of  a  column  of  thirty  inches  of 
mercury.  Tjie  pressure  of  the  atmosphere  acting  on  the  sur- 
face E  is  transmitted  by  the  mercury  to  the  surface  F,  and 
balances  the  elastic  force  just  mentioned. 

Let  the  position  of  the  surface  F  be  marked 
upon  the  tube,  and  let  mercury  be  poured 
into  the  longer  leg  at  A.  The  increased 
pressure  produced  by  the  weight  of  this  mer- 
cury will  be  transmitted  to  the  surface  F, 
and  will  prevail  over  the  elasticity  of  the 
confined  air :  this  surface  will  therefore  rise 
towards  D.  compressing  the  air  into  a  smaller 
space.  Let  the  mercury  continue  to  be 
poured  in  at  A,  until  the  surface  F  rise  to 
F',  Jiff.  10.,  the  middle  point  between  the 
end  D  of  the  tube,  and  its  first  position 
F.  The  air  included  is  thus  compressed 
into  half  its  former  dimensions,  and  its 
elasticity  will  be  measured  by  the  amount 
of  the  force  with  which  the  surface  F7  is 
pressed  upwards  against  it :  this  force  is  the 
weight  of  the  column  of  mercury  in  the  leg 
B  A,  above  the  level  of  F',  together  with  the 
weight  of  the  atmosphere  pressing  on  the  top 
G-  of  the  column.  Let  a  horizontal  line  be 
drawn  from  the  surface  F'  to  the  leg  B  A, 
and  let  the  column  G  II  be  measured ;  its 


Fig.  10. 


CHAP.    III.  DENSITY    OF    ATMOSPHERE.  187 

length  will  be  found  to  -  be  accurately  30  inches,  and  its 
weight  is  therefore  equal  to  the  atmospheric  pressure.  The 
force  with  which  F'  is  pressed  upwards  is  therefore  equal  to 
twice  the  atmospheric  pressure,  or  to  double  the  force  with 
which  F,  in  Jig.  9.,  was  pressed  upwards.  Hence  it  appears, 
that  the  elasticity  of  the  air  confined  in  the  space  D  F',Jig.  10., 
is  double  its  former  elasticity  when  filling  the  space  D  F,  Jig. 
9.  Thus,  when  the  air  is  compressed  into  half  its  volume,  its 
elasticity  is  doubled. 

In  like  manner,  if  mercury  be  poured  into  the  tube  A,  until 
the  air  included  in  the  shorter  leg  is  reduced  to  a  third  of  its 
bulk,  the  compressing  force  will  be  found  to  be  three  times  the 
atmospheric  pressure,  and  so  on. 

(134.)  That  the  elasticity  of  the  air  which  surrounds  us  is 
equal  to  the  weight  of  the  incumbent  atmosphere,  has  been 
proved  incidentally  in  the  preceding  experiment.  Indeed,  this 
is  a  proposition,  the  truth  of  which  must  appear  evident  upon 
the  slightest  consideration,  and  which  is  manifested  by  innu- 
merable familiar  effects.  If  the  elastic  force  of  the  air  around 
us  were  less  than  the  weight  of  the  incumbent  atmosphere,  it 
would  yield  and  suffer  itself  to  be  compressed  until  it  acquired 
an  elastic  force  equal  to  that  weight.  If  it  were  greater  in 
amount  than  the  weight  of  the  incumbent  atmosphere,  it  would 
overcome  that  weight,  and  would  press  the  atmosphere  upwards, 
until,  by  expanding,  its  elasticity  were  reduced  to  equality  with 
the  weight  of  the  atmosphere  ;  and  these  effects  are  continually 
going  forward.  The  incumbent  atmosphere  is  subject  to  con- 
tinual fluctuations,  in  weight,  as  will  hereafter  be  proved  ;  and 
the  lowest  stratum  of  air  which  surrounds  us  is  continually 
undergoing  corresponding  contractions  and  expansions,  ever 
accommodating  its  elasticity  to  the  pressure  which  it  sustains. 
Also  this  stratum  of  air  is  itself  subject  to  changes  of  elasticity, 
from  vicissitudes  of  temperature  proceeding  from  the  earth  to 
which  it  is  contiguous.  These  changes  produce  a  necessity 
for  expansion  and  contraction  in  it,  even  while  the  weight  of 
the  incumbent  atmosphere  remains  unchanged ;  but  the  full 
developement  of  this  last  consideration  belongs  to  the  theory  of 
heat  rather  than  to  our  present  subject. 

(135.)  An  open  vessel,  which  is  commonly  said  to  be  empty, 
is,  in  fact,  filled  with  air ;  and  when  any  solid  or  liquid  is  placed 
in  it,  so  much  of  the  air  is  expelled  as  occupied  the  space  into 
which  the  solid  or  liquid  entered.  If  such  a  vessel  be  closed 
by  a  lid  or  stopper,  the  pressure,  of  the  external  atmosphere  will 
act  upon  every  part  of  the  exterior  surface  with  an  intensity 
proportionate  to  its  weight.  The  air  which  is  enclosed  in  the 
vessel  will,  however,  act  on  the  interior  surface  with  an  inten- 
sity proportionate  to  its  elasticity.  According  to  what  has  been 


188 


A    TREATISE    OX    PNEUMATICS.  CHAP.    IV. 


already  explained,  this  elasticity  is  equal  to  the  pressure  ;  and, 
therefore,  there  is  a  force  tending  to  press  the  sides  of  the  ves- 
sel outwards,  exactly  equal  to  the  pressure  acting  on  the  exte- 
rior surface,  and  tending  to  press  them  inwards.  These  two 
forces  neutralize  each  other,  and  the  vessel  is  circumstanced 
exactly  as  if  neither  of  them  acted  upon  it. 

When  the  operation  and  properties  of  some  pneumatical  in- 
struments have  been  explained,  we  shall  have  occasion  to  notice 
many  other  effects  of  the  elasticity  of  air. 


CHAP.  IV. 

\ 

WEIGHT  OF  AIR. 

MAXIM  OF  THE  ANCIENTS. — ABHORRENCE  OF  A  VACUUM.— SUCTION. — 
GALILEO'S  INVESTIGATIONS. — TORRICELLI  DISCOVERS  THE  ATMOS- 
PHERIC PRESSURE. — THE  BAROMETER. — PASCAL'S  EXPERIMENT. — 
REQUISITES  FOR  A  GOOD  BAROMETER. — MEANS  OF  SECURING  THEM. 
— DIAGONAL  BAROMETER. — WHEEL  BAROMETER. — VERNIER. — USES 
OF  THE  BAROMETER. — VARIATION  OF  ATMOSPHERIC  PRESSURE. — 
WEATHER  GLASS.— RULES  IN  COMMON  USE  ABSURD. — CORRECT 
RULES. — MEASUREMENT  OF  HEIGHTS. — PRESSURE  ON  BODIES,— WHY 
NOT  APPARENT. — EFFECT  OF  A  LEATHER  SUCKER. — HOW  FLIES 
ADHERE  TO  CEILINGS,  AND  FISHES  TO  ROCKS. — BREATHING. — COM- 
MON BELLOWS. — FORGE  BELLOWS. — VENT-PEG. — TEA-POT.— KETTLE. 
INK-BOTTLES. — PNEUMATIC  TROUGH. — GUGGLING  NOISE  IN  DE- 
CANTING WINE. 

(136.)  IN  the  history  of  human  discovery,  there  are  few  more 
impressive  lessons  of  humility  than  that  which  is  to  be  collected 
from  the  records  of  the  progress  by  which  the  pressure  of  the 
atmosphere  which  surrounds  us,  and  the  manner  in  which  it  is 
instrumental  in  producing  some  most  ordinary  phenomena,  be- 
came known.  Looking  back  from  the  point  to  which  we  have 
now  attained,  and  observing  the  numerous  and  obvious  indica- 
tions of  this  effect  which  present  themselves  at  all  times,  and 
on  all  occasions,  nature  seems  almost  to  have  courted  the  phi- 
losopher to  the  discovery.  With  every  allowance  for  the  feeble- 
ness of  the  human  understanding,  and  for  the  disadvantages 
which  the  ancients  labored  under,  as  compared  with  more 
recent  investigators  ;  still  one  is  inclined  to  attribute  the  late- 
ness of  the  discovery  of  the  atmospheric  pressure  and  its  effects 
not  altogether  to  the  weakness  and  inadequacy  of  the  mental 
powers  applied  to  the  investigation.  There  seems  to  be  some- 
thing of  wilful  perverseness  and  obstinacy  instigating  men  to 
step  aside  from  that  course,  and  to  turn  their  minds  from  those 
instances  which  Nature  herself  continually  forces  upon  them. 


CHAP.  IV.     "NATURE  ABHORS  A  VACUUM."          ISO 

The  ancient  philosophers  observed,  that  in  the  instances 
which  commonly  fell  under  their  notice  space  was  always  filled 
by  a  material  substance.  The  moment  a  solid  or  a  liquid  was 
by  any  means  removed,  immediately  the  surrounding  air  rushed 
in  and  filled  the  place  which  it  deserted ;  hence  they  adopted 
the  physical  dogma  that  nature  abhors  a  vacuum.  Such  a  prop- 
osition must  be  regarded  as  a  figurative  or  poetical  expression 
of  a  supposed  law  of  physics,  declaring  it  to  be  impossible  that 
space  could  exist  unoccupied  by  matter. 

Probably  one  of  the  first  ways  in  which  the  atmospheric 
pressure  presented  itself  was  by  the  effect  of  suction  with  the 
mouth.  One  end  of  a  tube  being  immersed  in  a  liquid,  and  the 
other  being  placed  between  the  lips,  the  air  was  drawn  from 
the  tube  by  the  ordinary  process  of  inhaling.  The  water  was 
immediately  observed  to  fill  the  tube  as  the  air  retreated.  This 
phenomenon  was  accounted  for  by  declaring  that  "  Nature 
abhorred  a  vacuum,"  and  that  she  therefore  compelled  the  water 
to  fill  the  space  deserted  by  the  air. 

The  effects  of  suction  by  the  mouth  led,  by  a  natural  analogy, 
to  suction  by  artificial  means.  If  a  cylinder  be  open  at  both 
ends,  and  a  piston  playing  in  it  air-tight  be  moved  to  the  lower 
end,  upon  immersing  this  lower  end  in  water,  and  then  drawing 
up  the  piston,  an  unoccupied  space  would  remain  between  the 
piston  and  the  water.  "  But  nature  abhors  such  a  space,"  said 
the  ancients,  "  and  therefore  the  water  will  not  allow  such  a 
space  to  remain  unoccupied :  we  find  accordingly  that  as  the 
piston  rises  the  water  follows  it."  By  such  poetical  reasoning 
pumps  of  various  kinds  were  constructed. 

The  antipathy  entertained  by  nature  against  an  empty  space 
served  the  purposes  of  philosophy  for  a  couple  of  thousand 
years,  when  it  so  happened  that  some  engineers  employed  at 
Florence  in  sinking  pumps  had  occasion  to  construct  one  to 
raise  water  from  an  unusually  great  depth.  Upon  working  it 
they  fouild  that  the  water  would  rise  no  higher  than  about 
thirty-two  feet  above  -the  well.  Galileo,  the  most  celebrated 
philosopher  of  that  day,  was  consulted  in  this  difficulty  ;  and  it 
is  said  that  his  answer  was,  that  "  Nature's  abhorrence  of  a 
vacuum  extended  only  to  the  height  of  thirty-two  feet,  but  that 
beyond  this  her  disinclination  to  an  empty  space  did  not 
extend."  Some  writers*  deny  the  fact  of  his  having  given  this 
answer ;  others  admit  it,f  but  take  it  to  have  been  ironical.  It 
has  been  more  generally  taken  as  a  solution  seriously  intended.:}: 
It  appears,  however,  that  Galileo,  having  his  attention  thus 
directed  to  the  point,  soon  saw  the  absurdity  of  the  maxim,  that 

*  Enc3'clop8edia  Motropolitania,  Pneumatics. 

f  Biot,  Traite  de  Physique,  toino  i.  p.  69. 

j  Montucla,  Histoire  do  Mathematiques,  tome  ii.  p.  203. 


190  A    TREATISE    ON    PNEUMATICS.  CHAP.  IV. 

"  nature  abhors  a  vacuum,"  and  sought  to  account  for  the  phe- 
nomenon in  other  ways.  He  attributed  the  elevation  of  the 
water  to  an  attraction  exerted  upon  that  liquid  by  the  piston. 
This  attraction  he  conceived  to  have  a  determinate  intensity, 
and  when  such  a  column  of  water  was  raised  as  was  equal  in 
weight  to  the  whole  amount  of  the  attraction,  then  any  further 
elevation  of  the  water  by  the  piston  became  impossible. 

At  a  very  remote  period  air  was  known  to  possess  the  quality 
of  weight.  Aristotle  and  other  ancient  philosophers  expressly 
speak  of  the  weight  of  air.  The  process  of  respiration  is 
attributed  by  an  ancient  writer  to  the  pressure  of  the  atmos- 
phere forcing  air  into  the  lungs.  Galileo  was,  therefore,  fully 
aware  that  the  atmosphere l  possessed  this  property  ;  and  it  is 
not  a  little  surprising  that  when  his  attention  was  so  immediately 
directed  to  one  of  the  most  striking  effects  of  it,  he  was  unable 
to  perceive  the  connection. 

Some  writers*  affirm,  we  know  not  upon  what  authority,  that 
Galileo,  at  the  time  he  was  interrogated  respecting  the  limited 
elevation  of  water  in  a  common  pump,  was  aware  of  the  true 
cause  of  the  effect ;  but  that,  not  having  thoroughly  investigated 
the  subject,  he  evaded  the  question  of  the  engineers,  with  a 
view  to  conceal  his  knowledge  of  the  principle,  until  he  had 
carried  his  inquiry  to  a  more  satisfactory  result.  It  does  not, 
however,  appear  that  he  published  his  solution  of  the  problem. 
After  his  death  Torricelli,  his  pupil,  directed  his  attention  to  the 
same  problem.  He  argued  that  whatever  be  the  cause  which 
sustained  a  column  of  water  in  a  common  pump,  the  measure 
and  the  energy  of  that  power  must  be  the  weight  of  the  column 
of  water,  and,  consequently,  if  another  liquid  be  used,  heavier 
or  lighter,  bulk  for  bulk,  than  water,  then  the  same  force  must 
sustain  a  lesser  or  greater  column  of  such  liquid.  By  using  a 
much  heavier  liquid,  the  column  sustained  would  necessarily  be 
much  shorter,  and  the  experiment  in  every  way  more  man- 
ageable. 

He  therefore  selected  for  the  experiment  mercury,  the 
heaviest  known  liquid.  The  weight  of  mercury,  bulk  for  bulk, 
being  about  13£  times  that  of  water,  it  follows  that  the  height 
of  a  column  of  that  liquid  which  would  be  sustained  by  a  vacuum 
must  be  13i  times  less  than  the  height  of  a  column  of  water 
thus  sustained.  Hence  he  computed  that  the  height  of  the 
column  of  mercury  would  be  about  28  inches.  He  procured  a 
glass  tube,  A  B  (jig.  11.),  more  than  30  inches  in  length,  open 
at  one  end  A,  and  closed  at  the  other  end  B.  Placing  this  tube 
in  an  upright  position,  with  the  open  end  upwards,  he  filled  it 
with  mercury,  and  applying  his  finger  to  the  end  A,  so  as  to 

*  Biot,  Traite  de  Physique,  tome  i.  G9.     Young's   Natural  Philosophy,  voJ 
ii.  p.  354. 


CHAP.    IV. 


THE    BAROMETER. 


19. 


Fig.  11.  prevent  the  escape  of  the  mercury,  he  inverted  the 
tube,  plunging  the  end  A  into  a  cistern  C  D  (Jig.  12.), 
containing  mercury,  the  open  end  A  being  below  the 
surface  F  of  the  mercury  in  the  cistern,  and  no  air 
having  been  allowed  to  communicate  with  it.  Upon 
removing  the  finger,  therefore,  the  mercury  in  the 
cistern  came  in  immediate  contact  with  the  mercury 
in  the  tube.  Immediately  the  mercury  was  observed 
to  subside  from  the  top  of  the  tube,  and  its  surface 
gradually  to  descend  to  the  level  E,  about  28  inches 
above  the  mercury  in  the  cistern.  This  result  was 
what  Torricelli  anticipated,  and  clearly  showed  the 
absurdity  of  the  supposition  that  nature's  abhorrence 
of  a  vacuum  extended  to  the  height  of  32  feet.  Torri- 
celli soon  perceived  the  true  cause  of  this  phenomenon. 
The  atmospheric  pressure  acting  upon  the  surface  F, 
while  the  surface  E  was  protected  from  this  pressure 
by  the  closed  end  B  of  the  tube,  supported  the  weight 
of  the  column  E  F.  This  pressure  was  transmitted 
by  the  liquid  mercury  in  the  cistern  from  the  external 
surface  F  to  the  base  of  the  column  contained  in  the 
tube. 

This  experiment  and  its  explanation  soon  became  known  to 
philosophers  in  every  part  of  Europe,  and 
among  others,  it  attracted  the  notice  of  the 
celebrated  Pascal.  In  order  to  subject  the 
explanation  of  Torricelli  to  the  most  severe 
test,  Pascal  proposed  to  transport  a  tube  of  this 
kind  to  a  great  elevation  upon  a  mountain,  and 
argued  that  if  the  cause  which  sustained  the 
column  in  the  tube  were  the  weight  of  the 
atmosphere  acting  upon  the  external  surface 
of  the  mercury  in  the  cistern,  then  it  must  be 
expected  that  if  the  tube  was  elevated,  having 
a  less  and  a  less  quantity  of  atmosphere  above 
it,  the  column  sustained  by  the  weight  of  this 
incumbent  atmosphere  must  suffer  a  corres- 
ponding diminution  in  height.  He  accordingly 
directed  a  friend  residing  in  the  neighborhood 
of  a  mountain,  called  Puys  de  Dome,  near 
Auvergne,  to  ascend  that  mountain,  carrying 
with  him  the  apparatus  already  described. 
JD  This  was  accordingly  done,  and  the  height  of 
the  column  noted  during  the  ascent.  Con- 
formably to  the  principle  explained  by  Torri- 
celli, the  column  was  observed  gradually  to 
diminish  in  height,  as  the  elevation  of  the 


192  A    TREATISE    ON    PNEUMATICS.  CHAP.  IV. 

apparatus  was  increased.  The  same  experiment  was  repeated 
by  Pascal  himself,  with  similar  success,  upon  a  high  tower  in 
the  city  of  Paris. 

Meanwhile  other  effects  were  manifested  which  not  less 
unequivocally  proved  the  truth  of  Torricelli's  solution.  The 
apparatus  being  kept  for  a  length  of  time  in  a  fixed  position, 
the  height  of  the  column  was  observed  to  fluctuate  from  day  to 
day  between  certain  small  limits.  This  effect  was,  of  course, 
to  be  attributed  to  the  variation  of  the  weight  of  the  incumbent 
atmosphere,  arising  from  various  meteorological  causes. 

(137.)  The  apparatus  which  we  have  just  described  is,  in  fact, 
the  common  barometer.  By  the  principle  of  hydrostatics  it 
appears,  that  the  height  of  the  column  E  F,  sustained  by  the 
atmospheric  pressure,  will  be  the  same,  whatever  be  the  mag- 
nitude of  the  bore  of  the  tube.  If  we  suppose  the  section  of 
the  bore  to  be  equal  to  a  square  inch,  then  the  column  E  F  will 
be  pressed  upwards,  and  held  in  equilibrium  by  the  weight  of  a 
column  of  atmosphere  pressing  upon  a  square  inch  of  the  ex- 
ternal surface  F  ;  consequently  the  weight  of  the  column  E  F 
must  be  equal  to  the  weight  of  a  column  of  the  atmosphere 
whose  base  is  a  square  inch,  and  which  extends  from  the 
surface  of  the  mercury  in  the  cistern  to  the  top  of  the  atmos- 
phere. If  there  be  another  tube  whose  bore  is  only  half  a 
square  inch,  then  the  pressure  which  will  support  the  column 
in  it  will  be  that  of  a  similar  column  of  atmosphere,  whose  base 
is  half  a  square  inch  ;  such  pressure  then  will  only  be  half 
.the  amount  of  the  former,  and,  therefore,  will  only  sustain 
half  the  weight  of  mercury.  But  a  column  of  mercury  of 
half  the  weight,  having  a  base  of  half  the  magnitude,  must 
necessarily  have  the  same  height.  Hence  it  appears,  that  so 
long  as  the  atmosphere  presses  upon  a  given  magnitude  of  the 
surface  F,  with  the  same  intensity,  the  column  of  mercury  sus- 
tained in  the  tube  will  have  the  same  height,  whatever  be  the 
magnitude  of  its  bore. 

In  adapting  such  an  apparatus  as  this  to  indicate  minute 
changes  in  the  pressure  of  the  atmosphere,  there  are  many 
circumstances  to  be  attended  to,  which  we  propose  to  explain 
in  the  present  chapter,  so  far  as  they  are  necessary  to  render 
intelligible  the  general  principle  and  use  of  the  barometer. 

It  is,  in  the  first  place,  necessary  to  have  the  means  of  meas- 
uring exactly  the  height  of  the  column  E  F,  fig.  12. :  if  the 
surface  F  were  fixed,  and  the  tube  B  A  maintained  in  its  posi- 
tion, it  would  be  sufficient  to  mark  a  graduated  scale  upon  the 
tube,  indicating  the  number  of  inches  and  fractions  of  an  inch 
of  any  part  upon  it,  from  the  surface  F.  But  it  is  obvious  that 
this  will  not  be  the  case  when  the  pressure  of  the  atmosphere 
is  increased,  as  an  additional  quantity  of  mercury  is  forced  into 


CHAP.    IV.  THE    BAROMETER.  193 

the  tube,  and  consequently  an  equal  quantity  is  forced  out  of 
the  cistern.  While  the  surface  E  rises  towards  B,  the  surface 
F  therefore  descends,  and  the  distance  of  E  from  that  surface 
is  increased  by  both  causes.  A  graduated  scale  marked  upon 
the  tube  would  then  only  indicate  the  change  in  the  position  of 
the  surface  E,  but  would  not  show  the  change  in  the  length  of 
the  column  E  F,  so  far  as  that  change  is  affected  by  the  fall  of 
the  surface  F.  There  are  several  ways  in  which  this  defect 
may  be  remedied. 

If  the  instrument  be  not  required  to  give  extremely  accurate 
indications,  it  will  be  sufficient  to  use  a  tube  the  bore  of  which 
is  small  compared  with  the  magnitude  of  the  cistern.  In  this 
case  a  small  change  in  the  height  of  the  column  will  make  but 
a  very  inconsiderable  change  in  the  whole  quantity  of  mercury 
in  the  cistern,  and,  therefore,  will  produce  a  very  minute  effect 
upon  the  position  of  the  surface  F.  If  such  a  change  in  the 
level  F  be  so  small  as  to  affect  the  indications  of  the  instrument 
in  a  degree  which  is  unimportant  for  the  purposes  to  which  it 
is  intended  to  be  applied,  the  surface  F  may  be  regarded  as 
fixed,  and  the  whole  change  in  the  height  of"  the  column  may 
be  taken  to  be  represented  by  the  change  in  the  position  of  the 
level  E.  All  ordinary  barometers  are  constructed  in  this 
manner. 

But  it  is  not  difficult  to  adjust  a  scale  upon  a  tube  which  will 
give  with  accuracy  the  actual  variation  in  the  length  of  the 
•column  by  means  of  the  change  in  the  level  of  the  surface  E. 
Let  us  suppose  that  the  cistern  C  D  has  a  flat  horizontal  bottom 
and  perpendicular  sides,  and  that  the  magnitude  of  the  bottom 
bears  a  certain  known  proportion  to  the  bore  of  the  tube.  Sup- 
pose this  proportion  be  that  of  one  to  a  hundred.  If  the  pres- 
sure of  the  atmosphere  increase,  so  as  to  cause  the  column  of 
mercury  sustained  in  the  tube  to  be  increased  in  height  by  one 
inch,  then  as  much  mercury  as  fills  one  inch  of  the  tube  will  be 
withdrawn  from  the  cistern  ;  but  as  the  base  of  the  cistern  is 
one  hundred  times  greater  than  the  bore  of  the  tube,  it  is  evi- 
dent that  this  inch  of  mercury  in  the  tube  would  only  cause  a 
fall  of  the  hundredth  of  an  inch  in  depth  of  the  mercury  in  the 
vessel:;  consequently  it  follows  that  the  increased  elevation  of 
an  inch  in  the  column  produces  a  depression  of  a  hundredth  of 
an  inch  in  the  surface  F.  Thus  it  appears,  that  the  increased 
length  of  the  column  E  F  is  produced  by  the  surface  F  falling 
through  the  one  hundredth  of  an  inch,  while  the  surface  E  rises 
through  99  hundredth  parts  of  an  inch.  The  same  will  be  true 
whatever  change  takes  place  in  the  height  of  the  column.  We 
may  therefore  infer,  generally,  that  whatever  variation  may  be 
produced  in  the  surface  E,  the  consequent  variation  produced 
in  the  height  of  the  column  is  greater  by  a  ninety-ninth  part. 


194 


A    TREATISE    ON    PNEUMATICS. 


CHAP.    IV. 


If  then  the  top  be  so  graduated  that  a  portion  of  it,  the  length 
of  which  is  one  hundredth  part  less  than  an  inch,  be  marked  as 
an  inch,  and  all  other  divisions  and  subdivisions  marked  accord- 
ing to  the  same  proportion,  then  the  indications  will  be  as 
accurate  as  if  the  surface  F  were  fixed  ;  the  tube  being  divided 
accurately  into  inches  and  parts  of  an  inch. 

The  barometer  is  represented  mounted  and  fur- 
Fig.  13.  nished  with  a  scale,  in  Jig.  13.  The  glass  tube  is 
surrounded  by  one  of  brass,  in  which  there  is 
an  aperture  cut  at  D  E,  of  such  a  length  and  at 
such  a  height  above  the  cistern,  as  to  include  all 
that  space  through  which  the  level  of  the  mercury 
in  the  tube  usually  varies  in  the  place  in  which  the 
barometer  is  intended  to  be  used.  In  these  coun- 
tries the  level  of  the  mercury  never  falls  below  28 
inches,  nor  rises  above  31  inches  ;  consequently  a 
space  somewhat  exceeding  these  limits  will  be 
sufficient  for  the  opening  D  E.  The  tube  is  per- 
manently connected  with  the  cistern  A  B,  and  a 
scale  is  engraved  upon  the  brass  tube  near  the 
aperture  D  E,  to  indicate  the  fractions  of  the 
height  of  the  mercury  in  the  tube. 

There  is  another  method  of  avoiding  the  diffi 
culty  arising  from  the  change  in  the  level  of  the 
surface  of  the  mercury  in  the  cistern,  used  in  the 
barometer  here  represented.  The  bottom  of  the 
cistern  moves  within  it  in  such  a  manner  as  to  pre- 
vent the  mercury  from  escaping,  and  a  screw  is 
inserted  at  V,  by  turning  which  the  bottom  of  the 
cylinder  is  slowly  elevated  or  depressed.  An 
ivory  index  is  attached  to  the  top  of  the  cylinder, 
which  is  presented  downwards  and  brought  to  a 
fine  point,  so  as  to  mark  a  fixed  level.  When  an  observation 
is  made  with  the  barometer,  the  screw  V  is  turned  until  the 
surface  is  brought  accurately  to  the  point  of  the  index,  by  rais- 
ing or  lowering  the  bottom  according  as  the  surface  is  below 
or  above  that  point.  It  follows,  therefore,  that  whenever  an 
observation  is  made  with  this  instrument,  the  surface  of  the 
mercury  always  stands  at  the  same  level,  and  therefore  the  di- 
visions upon  the  scale  C  F  represent  the  actual  change  of 
height  in  the  barometric  column. 

Since  the  column  of  mercury  sustained  in  the  barometric 
tube  is  taken  to  represent  the  pressure  of  the  atmosphere,  it  is 
clear  that  no  air  or  other  elastic  fluid  should  occupy  the  part  of 
the  tube  above  the  mercury.  To  avoid  such  a  cause  of  error  is 
not  so  easy  or  obvious  as  may  at  first  appear.  Mercury,  as  it 


CHAP.    IV.  THE    BAROMETER.  195 

exists  in  the  ordinary  state,  frequently  contains  air  or  other 
elastic  fluids  combined  with  it,  and  which  are  maintained  in  it 
by  the  atmospheric  pressure,  to  which  it  is  usually  subject. 
When  it  has  subsided,  however,  in  the  barometric  tube,  it  is 
relieved  from  that  pressure,  and  the  elastic  force  of  such  air  as 
may  be  lodged  in  the  mercury  being  relieved  from  the  pressure 
which  confined  it  there,  it  will  make  its  escape  and  rise  to  the 
surface,  finally  occupying  the  upper  part  of  the  tube,  and  ex- 
erting a  pressure  upon  the  surface  of  the  column  by  means  of 
its  elasticity.  Such  a  pressure  will  then  assist  the  weight  of 
the  column  of  mercury  in  balancing  the  atmospheric  pressure, 
and  consequently  a  column  of  less  height  will  balance  the 
atmosphere  than  if  the  upper  part  of  the  tube  were  free  from 
air.  To  remove  this  cause  of  error  it  is  necessary  to  adopt 
means  of  purifying  the  mercury  used  in  the  barometer  from  all 
elastic  fluids  which  may  be  combined  with  it. 

The  fact,  that  the  application  of  heat  gives  energy  to  the 
elastic  force  of  gases,  enables  us  easily  to  accomplish  this. 
For  if  the  mercury  be  heated,  the  particles  of  air  or  other  elas- 
tic fluids  which  are  combined  with  it  acquire  such  a  degree  of 
elasticity,  that  they  dilate  and  rise  to  the  surface,  and  there 
escape  in  bubbles.  The  same  process  of  heating  serves  to 
expel  any  liquid  impurities  with  which  the  mercury  may  be 
combined.  These  are  converted  into  vapor,  and  escape  at  the 
surface. 

The  presence  of  an  elastic  fluid  at  the  top  of  the  tube  is  thus 
removed  so  far  as  such  fluid  can  proceed  from  the  mercury. 
But  it  is  also  found  that  small  particles  of  air  and  moisture  are 
liable  to  adhere  to  the  interior  surface  of  the  glass  ;  and  when 
the  mercury  is  introduced,  and  a  vacuum  produced  at  the  top 
of  the  tube,  these  particles  of  air  dilate,  and,  rising,  lodge  at 
the  top,  and  vitiate  the  vacuum  which  ought  to  be  there  ;  the 
particles  of  moisture  also  evaporate  and  rise  likewise,  both  pro- 
ducing an  aeriform  fluid  in  the  chamber  above  the  surface  of 
the  mercury,  which  presses  upon  that  surface  with  an  elastic 
force,  and  produces  a  corresponding  diminution  in  the  height 
of  the  column  of  quicksilver  sustained  by  the  atmosphere,  as 
already  explained.  This  imperfection  may  be  avoided  by  pre- 
viously heating  the  tube.  The  particles  of  air  which  adhere  to 
its  inner  surface  being  thus  expanded  by  heat,  will  fly  off  by 
their  elastic  force,  and  the  particles  of  moisture  will  be  con- 
verted into  vapor,  and  likewise  disengaged  from  the-surface. 

All  the  effects  now  explained  may  be  produced  by  filling  the 
tube  with  mercury  in  the  first  instance,  and  then  boiling  the 
liquid  in  it,  which  may  be  easily  accomplished.  The  heat  will 
not  only  expel  all  liquid  and  gaseous  impurities  from  the  mer- 
cury itself,  bi.il  abo  .,111  disengage  them  from  the  inner  surface 


196  A   TREATISE    ON    PNEUMATICS,  GBAP.    IV. 

of  the  tube.  These  precautions  being  taken,  the  column  of 
mercury  sustained  in  the  tube  will  indicate  by  its  weight  the 
true  amount  of  the  atmospheric  pressure.  But  in  order  to  be  able 
to  compare  the  result  of  any  one  barometer  with  any  other,  it 
is  necessary  that  the  weights  of  equal  bulks  of  the  liquid  mer- 
cury used  in  both  cases  should  be  the  same  ;  and  for  this  pur- 
pose we  must  be  assured  that  the  mercury  used  is  pure,  and 
not  combined  with  other  substances.  We  have  just  seen  how- 
all  substances  in  the  liquid  or  gaseous  form  may  be  extracted 
from  it.  Impurities  may  still,  however,  be  suspended  in  it  in 
the  solid  form.  To  remove  these  it  is  only  necessary  to  en- 
close the  mercury  in  a  small  bag  of  chamois  leather:  upon 
pressing  this  bag  the  quicksilver  will  pass  freely  through  its 
pores,  and  any  minute  solid  impurities  which  may  be  contained 
in  the  mercury  will  remain  in  the  bag.  Pure  and  homogeneous 
mercury  being  thus  obtained,  we  have  advanced  another  step 
towards  the  certainty  that  the  indications  of  diiferent  barome- 
ters may  correspond  ;  but  there  is  still  one  other  cause  of  dis- 
cordance to  be  attended  to.  Suppose  a  barometer  to  be  used 
in  Paris,  and  another  in  London,  at  a  time  when  the  pressure 
of  the  atmosphere  in  both  places  is  the  same,  but  the  tempera- 
ture of  the  air  at  Paris  is  higher  than  the  temperature  of  London. 
The  mercury  in  the  one  barometer  will  have  a  higher  tempera- 
ture than  the  mercury  in  the  other.  Now  it  is  well  known 
that  when  mercury  or  any  other  body  is  heated,  its  dimensions 
increase.  In  other  words,  bulk  for  bulk,  it  becomes-  lighter. 
Consequently,  of  two  columns  equal  in  weight,  that  which  has 
the  higher  temperature  will  have  the  greater  altitude.  Hence 
it  appears,  that  under  the  circumstances  supposed,  at  a  time 
when  the  atmospheric  pressure  is  the  same  in  London  as  *t 
Paris,  the  barometer  at  the  latter  place  will  be  higher  than  at 
the  former.  To  guard  against  this  source  of  error  it  is  neces- 
sary, in  making  barometric  observations,  to  note  at  the  same 
time  the  contemporaneous  indications  of  the  thermometer. 
Tables  are  computed  showing  the  changes  in  the  height  of  the 
mercury  corresponding  to  given  differences  of  temperature.  It 
is  evident  that  in  comparing  the  results  of  the  same  barometer 
observed  at  diiferent  times,  it  is  equally  necessary  to  note  the 
difference  of  temperature,  and  to  allow  for  its  effects.  This, 
however,  is  a  refinement  of  accuracy  which  is  not  attended  to, 
except  in  observations  made  for  philosophical  purposes. 

(138.)  One  of  the  difficulties  attending  barometric  observa- 
tions arises  from  the  very  minute  changes  produced  in  the 
height  of  the  column  by  slight  variations  in  the  atmospheric 
pressure.  The  whole  play  of  the  upper  surface  of  the  column, 
in  the  most  extreme  cases,  does  not  exceed  three  or  four  inches 
in  a  given  place  ;  and  mercury  being  a  very  heavy  fluid,  a  vari- 


DIAGONAL    BAROMETER. 


1U7 


ation  in  the  pressure  of  the  atmosphere,  of  sensible  amount, 
may  produce  scarcely  any  perceptible  change  in  the  height  of 
the  column.  One  of  the  most  obvious  remedies,  at  first  view, 
would  seem  to  be  the  use  of  a  fluid  lighter  than  mercury.  In 
the  same  proportion  as  the  fluid  is  lighter  will  the  change  in 
the  height  of  the  column  by  a  given  change  in  the  pressure  of 
the  atmosphere  be  greater ;  but  there  are  difficulties  of  a  dif- 
ferent kind  which  altogether  preclude  the  use  of  other  fluids. 
The  lighter  liquids  are  much  more  susceptible  of  evaporation, 
and  the  surface  of  the  liquid  in  the  tube,  being  relieved  from 
the  atmospheric  pressure,  offers  no  resistance  to  the  process  of 
evaporation.  The  consequence  is,  that  any  liquid,  except  mer- 
cury, would  produce  a  vapor,  which,  occupying  the  top  of  the 
tube,  would  press  by  its  elastic  force  upon  the  surface,  and  co- 
operate with  the  weight  of  the  suspended  column  in  balancing 
the  atmospheric  pressure.  Even  from  mercury  we  have  reason 
to  know  that  a  vapor  rises  which  is  present  in  the  upper  part 
of  the  tube,  but  this  pressure  exerts  no  power  which  can 
introduce  inaccuracy  to  any  sensible  extent  into  our  conclu- 
sions. 

(139.)  A  form  is  sometimes  adopted,  called  the  diagonal 
barometer,  for  the  purpose  of  increasing  the  range  of  the  mer- 
cury in  the  tube.  This  is  represented  in  Jig.  14.,  where  A  C  B 

Fig.  14. 


represents  the  barometric  tube.  C  is  a  point  at  a  distance  above 
the  surface  of  the  mercury  in  the  cylinder  less  than  the  height 
of  28  inches.  The  space  C  D  includes  the  range  which  the 


198 


A    TREATISE    ON    PNEUMATICS. 


CHAP.    IV. 


mercury  would  have  if  the  tube  were  vertical ;  but  at  C  the  tube 
is  bent  obliquely  in  the  direction  C  B,  having  a  sufficient  length 
to  bring  the  extremity  B  to  the  same  level  as  D.  The  mercury 
which,  had  the  tube  been  vertical,  would  range  between  C  and 
D,  will  now  have  its  play  extended  through  the  greater  space 
C  B  ;  consequently  the  magnitude  of  any  part,  however  small, 
will  be  increased  in  the  proportion  of  the  line  C  D  to  the  line 
C  B.  Thus,  if  C  D  be  4  inches,  and  C  B  12  inches,  then  every 
change  in  the  position  of  the  surface  of  the  mercury,  produced 
by  a  change  in  the  atmospheric  pressure,  will  be  three  times  as 
great  in  the  diagonal  barometer  as  it  would  be  in  the  vertical 
one. 

(140.)  Another  contrivance  for  enlarging  the  scale,  which  is 
more  frequently  used,  and  for  common  domestic  purposes  at- 
tended with  some  convenience,  is  represented  mfg.  15.  This 
is  called  the  wheel  barometer.  The  barometric 
Fig.  15.  tube  is  here  bent  at  its  lower  extremity  B,  and 
turned  upwards  towards  C.  The  atmospheric 
pressure  acts  upon  the  surface  F,  and  sustains 
a  column  of  mercury  in  the  tube  B  A,  which  is 
above  the  level  of  F.  The  bore  of  the  tube 
being  in  this  case  equal  in  every  part  of  its 
length,  it  is  clear  that  through  whatever  space 
the  surface  E  falls,  the  surface  F  will  rise,  and 
vice  versa-  Hence  it  is  obvious  that  the  varia- 
tion in  the  height  of  the  barometric  column 
will  always  be  double  the  change  in  the  height 
of  either  surface  E  or  F  ;  for  if  the  surface  F 
fall,  the  surface  E  must  rise  through  the  same 
space.  They  are  thus  receding  from  each 
other  at  the  same  rate,  and  therefore  their  mu- 
tual distance  will  be  increased  by  the  space 
through  which  each  moves,  or  by  double  the 
space  through  which  one  of  them  moves.  In 
the  same  manner,  if  F  rise,  E  must  fall,  the  two 
points  mutually  approaching  each  other  at  the 
same  rate  ;  so  that  the  distance  between  them 
will  be  diminished  by  the  space  through  which 
each  moves,  or  by  double  the  space  through 
which  one  of  them  moves.  The  change,  there- 
fore, in  the  height  of$ie  barometric  column  will  always  be 
double  the  change  in  the  position  of  the  level  F. 

Upon  the  surface  at  F  there  floats  a  small  ball  of  iron,  sus- 
pended by  a  string,  which  is  carried  over  a  pulley  or  small 
wheel  at  P,  and  counterpoised  by  the  weight  at  W,  less  in 
amount  than  the  weight  of  the  iron  ball.  When  the  surface  F 
rises,  the  iron  ball,  being  buoyant,  will  be  raised  with  it,  and  the 


CHAP.    IT.  WHEEL    BAROMETER.  199 

counterpoise  W  will  fall ;  and  when  the  surface  F  falls,  the 
weight  of  the  iron  ball,  being  greater  than  the  weight  of  the 
counterpoise,  will  cause  it  to  descend  with  the  descending  sur- 
face, and  to  draw  the  counterpoise  W  up.  It  is  evident  that, 
through  whatever  space  the  iron  ball  thus  moves  in  ascending 
or  descending,  an  equal  length  of  the  string  will  pass  over  the 
wheel  P.  Now  this  string  rests  in  a  groove  of  the  wheel,  in 
such  a  manner  that,  by  its  friction,  it  causes  the  wheel  to  re- 
volve, and,  consequently,  the  revolution  of  this  wheel  indicates 
the  length  of  the  string  which  passes  over  its  groove,  which 
length  is  equal  to  the  change  in  the  level  of  the  surface  F. 
Upon  the  centre  of  this  wheel  P  an  index  H  is  placed,  which, 
like  the  hand  of  a  watch,  plays  upon  a  graduated  circular  plate. 
Let  us  suppose  that  the  circumference  of  the  wheel  P  is  two 
inches,  then  one  complete  revolution  of  this  wheel  will  corre- 
spond to  a  change  of  2  inches  in  the  level  F,  and,  therefore,  to 
a  change  of  4  inches  in  the  barometric  column.  But  in  one 
revolution  of  the  wheel  P  the  hand  or  index  H  moves  complete- 
ly round  the  circle :  hence  the  circumference  of  this  circle 
corresponds  to  a  change  of  4  inches  in  the  barometric  column. 
Now,  the  circular  plate  may  easily  be  made  so  that  its  cir- 
cumference shall  measure  40  inches  ;  consequently  10  inches  of 
this  circumference  will  correspond  to  1  inch  of  the  column,  and 
1  inch  of  the  circumference  will  correspond  to  the  tenth  of  an 
inch  of  the  column.  In  this  way  variations  in  the  height  of 
the  column  amounting  to  the  tenth  of  an  inch  are  indicated  by 
a  motion  of  the  hand  H  over  1  inch  of  the  circumference  of  the 
plate.  By  further  subdivision  a  still  greater  accuracy  may  be 
obtained. 

In  this  form  of  the  barometer  it  is  evident  that  the  prepon- 
derance of  the  iron  ball  assists  the  atmospheric  pressure  in 
sustaining  the  column.  This  cause  of  error,  however,  may  be 
diminished  almost  indefinitely  by  making  the  preponderance  of 
the  ball  over  the  counterpoise  W  barely  sufficient  to  overcome 
the  friction  of  the  wheel  P.  Again,  when  the  atmosphere  is 
diminished  in  weight,  and  when  the  surface  F  has  a  tendency 
to  rise,  it  is  compelled  to  raise  the  ball ;  and  there  is  this  ob- 
vious limit  to  the  indications  of  the  instrument,  namely,  that  a 
change  so  slight  that  the  difference  of  pressure  will  not  ex- 
ceed the  force  necessary  to  elevate  the  ball  will  fail  to  be 
indicated. 

(141.)  For  scientific  purposes,  the  vertical  barometer  is  pref- 
erable to  every  other  form  of  that  instrument.  In  the  oblique 
barometer  the  termination  of  the  mercurial  column  is  subject 
to  some  uncertainty  arising  from  the  level  of  the  mercury  not 
being  perpendicular  to  the  direction  of  the  tube.  In  the  wheel 
barometer  there  are  several  sources  of  error  which,  though  so 


4- 


200  A    TREATISE    ON    PNEUMATICS.  CHAP.    IV. 

small  in  amount  as  not  to  injure  it  for  domestic  or  popular  use, 
yet  are  such  as  to  render  it  altogether  unfit  for  scientific  in- 
quiry. A  contrivance  called  a  Vernier,  for  noting  extremely 
small  changes,  is  usually  applied  to  the  vertical  barometer,  and 
supplies  the  place  of  an  enlarged  scale.  It  consists  of  a  small 
graduated  plate  which  is  movable  by  a  screw  or  otherwise,  and 
which  slides  on  the  divided  scale  of  the  barometer.  By  means 
of  this  subsidiary  scale,  we  are  enabled  to  estimate  magnitudes 
on  the  principal  scale,  amounting  to  very  small  fractions  of  its 
smallest  divisions. 

The  principle  of  the  vernier  is  easily  explained. 
Fig.  16.  Let  B  A,  Jig.  16.,  represent  the  scale  of  the  barometer 
„.         extending  through  three  inches,  and  divided  to  tenths 
of  an  inch.     Let  C  D  be  the  sliding  scale  of  the  ver- 
nier, equal  in  length  to  eleven  divisions  of  the  principal 
scale,  and  divided  into  ten  equal  parts. 

Thus  each  division  of  the  vernier  will  be  the  tenth 
of  eleven  divisions  of  the  instrument ;  that  is,  it  will 
be  the  tenth  part  of  11  tenths  of  an  inch  ;  but  11  tenths 
of  an  inch  is  the  same  as  110  hundredths,  and  the 
tenth  part  of  this  is  11  hundredths.  Thus  it  appears 
that  one  division  on  the  vernier  is  in  this  case  11 
hundredth  parts  of  an  inch.  Now  one  division  on  the 
instrument  being  a  tenth  of  an  inch,  or  10  hundredths 
of  an  inch,  it  is  evident  that  a  division  on  the  vernier 
will  exceed  a  division  on  the  instrument  by  the  hun- 
dredth part  of  an  inch ;  for  if  we  take  10  hundredths 
from  11  hundredths,  the  remainder  will  be  1  hun- 
dredth. 

Let  us  suppose  that  the  vernier  is  placed  so  that  its 
3  lowest  division,  marked  10,  shall  coincide  with  the 
lowest  division  on  the  instrument  marked  28  ;  then  the 
first  division  of  the  vernier  marked  0  will  coincide  with 
the  division  of  the  instrument  next  above  the  29th. 
The  division  marked  1  on  the  vernier  will  then  be  a 
little  below  the  division  marked  29  on  the  scale,  and 
_0the  distance  between  these  will  be  the  hundredth  of 
an  inch,  as  already  explained.  The  division  marked 
2  of  the  vernier  will  be  a  little  below  the  division 
marked  9  on  the  scale,  and  the  distance  below  it  will  be  2  hun- 
dredth parts  of  an  inch  ;  because  two  divisions  of  the  vernier 
exceed  two  divisions  of  the  scale  by  that  amount.  In  like 
manner,  the  division  marked  3  on  the  vernier  will  be  below  the 
division  marked  8  on  the  scale  by  3  hundredths  of  an  inch,  and 
so  on. 

Let  us  suppose  that  the  mercury  is  observed  to  stand  at  a 
height  greater  than  29  inches  and  5  tenths,  but  less  than  29 


CHAP.    IV. 


VERNIER. 


201 


inches  and  6  tenths.  Its  level  being  expressed  by  the  dotted 
line  M,  Jig.  17.,  let  the  vernier  now  be  moved  on 
Fig-  17.  the  scale  until  its  highest  division  0  exactly  coin- 
cides with  the  level  of  the  mercury.  On  compar- 
ing the  several  divisions  of  the  vernier  with  those 
of  the  instrument,  let  us  suppose  that  we  find  that 
the  division  marked  4  on  the  vernier  coincides  with 
that  marked  1  on  the  instrument  ;  then  the  dis- 
tance from  the  level  of  the  mercury  M  to  the  next 
division  below  it,  marked  5,  will  be  4  hundredth 
parts  of  an  inch  ;  for  the  distance  of  the  division 
marked  3  on  the  vernier  above  the  division  marked 
2  on  the  instrument  is  1  hundredth  of  an  inch,  be- 
cause it  is  the  difference  between  a  division  of  the 
vernier  and  a  division  of  the  instrument.  Again, 
the  distance  of  the  division  of  the  vernier,  marked 
2  above  the  division  of  the  instrument  marked  3, 
is  2  hundredths  of  an  inch,  and  the  distance  of  the 
division  of  the  vernier  marked  1  above  the  division 
of  the  instrument  marked  4,  is  3  hundredths  of  an 
inch.  In  like  manner  the  division  of  the  vernier 
marked  0  is  distant  from  the  division  of  the  instru-  • 
ment  marked  5  by  4  hundredths  of  an  inch.  This 
will  be  manifest  by  considering  what  has  been 
~ILl_  10  already  explained.  In  general  we  are  to  observe 
r  what  division  of  the  vernier  coincides  most  nearly 
with  any  division  of  the  instrument,  and  the  figure 
which  marks  that  division  of  the  vernier  will  ex- 
press the  number  of  hundredths  of  an  inch  in  the 
distance  of  the  level  of  the  mercury  from  the  next 
division  of  the  instrument  below  it. 

(142.)  The  most  immediate  use  of  the  barometer  for  scientific 
purposes  ;s  to  indicate  the  amount  and  variation  of  the  at- 
mospheric pressure.  These  variations,  being  compared  with 
other  meteorological  phenomena,  form  the  scientific  data  from 
which  various  atmospheric  appearances  and  effects  are  to  be 
deduced. 

The  fluctuations  in  the  pressure  of  the  atmosphere  being  ob- 
served in  connection  with  changes  in  the  state  of  the  weather, 
a  general  correspondence  is  supposed  to  prevail  between  these 
effects.  Hence  the  barometer  has  been  called  a  weather  glass. 
Rules  are  attempted  to  be  established,  by  which,  from  the 
height  of  the  mercury,  the  coming  state  of  the  weather  may  be 
predicted,  and  we  accordingly  find  the  words  "  Rain,"  "  Fair," 
"  Changeable,"  "  Frost,"  &c.,  engraved  on  the  scale  attached  to 
common  domestic  barometers  ;  as  if,  when  the  mercury  stands 
at  the  heigld  marked  by  these  words,  the  weather  is  always 


A    TREATISE    ON    PNEUMATICS.  CHAP     IV 


Hi  '  ta 


abha,  ,  ef 

The  variation  in  the  altitude  of  the  barometer  in  a  cri™, 


that  when  the  mercury  is  very  low,  and  therefore  the  at 
phere  very  hght,  hif  h  winds  and  sto'rms  may  be  expected 

*     at  least  to 


of  fei   TeTthitethS?fi  °f  thepmerCUry  indicates  the 
weather?  ff  °f  Jt  Sh°WS  the  aPProach  of 

unl™l?TybreefeXrPr!nlneto  dST  vfi  ^{J0^^  considerations  j  which  will  bo 


osphcro,  which 


CHAP.    IV.  WEATHER    GLASS.  JJUtf 

2.  In  sultry  weather,  the  fall  of  the  mercury  indicates  coming 
thunder.     In  winter,  the  rise  of  the  mercury  indicates  frost.     In 
frost,  its  fall  indicates  thaw  ;  and  its  rise  indicates  snow. 

3.  Whatever  change  of  weather  suddenly  follows  a  change 
in  the  barometer  may  be  expected  to  last  but  a  short  time. 
Thus,  if  fair  weather  follow  immediately  the  rise  of  the  mercu- 
ry, there  Avill  be  very  little  of  it ;  and,  in  the  same  way,  if  foul 
weather  follow  the  fall  of  the  mercury,  it  will  last  but  a  short 
time. 

4.  If  fair  weather  continue  for  several  days,  during  which 
the  mercury  continually  falls,  a  long  succession  of  foul  weather 
will  probably  ensue  ;  and  again,  if  foul  weather  continue  for 
several  days,  while  the  mercury  continually  rises,  a  long  suc- 
cession of  fair  weather  will  probably  succeed. 

5.  A  fluctuating  and  unsettled  state  in  the  mercurial  column 
indicates  changeable  weather. 

The  domestic  barometer  would  become  a  much  more  useful 
instrument,  if,  instead  of  the  words  usually  engraved  on  the 
plate,  a  short  list  of  the  best  established  rules,  such  as  the 
above,  accompanied  it,  which  might  be  either  engraved  on  the 
plate,  or  printed  on  a  card.  It  would  be  right,  however,  to  ex- 
press the  rules  only  with  that  degree  of  probability  which  ob- 
servation of  past  phenomena  has  justified.  There  is  no  rule 
respecting  these  effects  which  will  hold  good  with  perfect  cer- 
tainty in  every  case. 

(143.)  One  of  the  most  important  scientific  uses  to  which 
the  barometer  has  been  applied  is  the  measuring  of  heights. 
If  the  atmosphere,  like  a  liquid,  were  incompressible,  this  prob- 
lem would  be  very  simple.  The  pressure  on  the  mercury  in 
the  cistern  would  be  equally  diminished  in  ascending  through 
equal  heights.  Thus,  if  the  pressure  produced  by  an  ascent 
of  10  feet  were  equivalent  to  the  weight  of  one  inch  of  mercury, 
then  the  column  would  fall  one  inch  in  ascending  that  height. 
It  would  fall  two  inches  in  ascending  20  feet,  three  in  ascend- 
ing 30  feet,  and  so  on.  To  find,  therefore,  the  perpendicular 
height  of  the  barometer  at  any  time  above  its  position  at  any 

val  between  its  inceptive  and  maximum  velocity.  We  have  supposed  the  size  of 
the  drop  and  the  density  of  the  air  to  remain  the  same.  The  increasing  density 
of  the  medium  retards  the  velocity  of  the  drop,  and  causes  it  to  press  the  air  with 
a  force  a  little  superior  to  its  own  weight  during  this  retardation,  from  the  time  it 
begins  till  the  descent  is  completed,  when  the  air  is  relieved  from  this  pressure. 

If  the  foregoing  views  are  correct,  the  atmospheric  pressure  will  be  affected, 
though  in  different  ways,  by  the  quantity  of  aqueous  vapor  in  the  atmosphere,  by 
the  quantity  of  that  which,  either  in  the  form  of  clouds,  rain,  snow,  or  hail,  is  de- 
scending without  having  yet  attained  its  maximum  velocity,  and  by  the  quantity 
which  has  already  attained  this  velocity.  Hence  the  mercury  of  the  barometer 
may  be  depressed  in  consequence  of  the  descent  of  drops  in  their  first  stage,  long 
before  they  reach  the  earth  ;  and  this  effect  will  be  modified  by  the  different  por- 
tions in  the  subsequent  stages,  as  well  aa  by  other  causes  which  affect  the  atmos- 
pheric pressure. — AM.  ED. 


204  A    TREATISE    ON    PNEUMATICS.  CHAP.    IV. 

other  time,  it  would  be  only  necessary  to  observe  the  differ- 
ence between  the  altitude  ofthe  mercury  in  both  cases,  and  to 
allow  10  feet  for  every  inch  of  mercury  in  that  difference  ;  and 
a  similar  process  would  be  applicable  if  an  inch  of  mercury  cor- 
responded to  any  other  number  of  feet. 

But  this  explanation  proceeds  on  the  supposition,  that  in 
ascending  through  equal  heights,  the  barometer  leaves  equal 
weights  of  air  below  it.  Suppose  in  ascending  10  feet  the 
mercury  is  observed  to  fall  the  hundredth  of  an  inch,  then  it 
follows,  that  the  air  left  below  the  barometer  in  such  an  ascent 
has  a  weight  equal  to  the  one  hundredth  of  an  inch  of  mercury. 
Now,  in  ascending  the  next  10  feet,  the  air  which  occupies  that 
space,  having  a  less  weight  above  it,  will  be  less  compressed, 
and  consequently  within  that  height  of  10  feet  there  will  be 
contained  a  less  quantity  of  air  than  was  contained  in  the  first 
10  feet  immediately  below  it.  In  this  second  ascent  the  mer- 
cury will,  therefore,  fall,  not  the  hundredth  of  an  inch,  but  a 
quantity  as  much  less  than  the  hundredth  of  an  inch  as  the 
quantity  of  air  contained  in  the  second  10  feet  of  height  is  less 
than  the  quantity  of  air  that  is  contained  in  the  first  10  feet  of 
height.  In  like  manner  in  ascending  the  next  10  feet  a  still 
less  quantity  of  air  will  be  left  below  the  instrument,  and  the 
mercury  will  fall  in  a  proportionally  less  degree. 

If  the  only  cause  affecting  density  of  the  air  were  the  com- 
pression produced  by  the  weight  of  the  incumbent  atmosphere, 
it  would  be  easy  to  find  the  rule  by  which  a  change  of  altitude 
might  be  inferred  from  an  observed  change  of  pressure.  Such 
a  rule  has  been  determined,  and  is  capable  of  being  expressed 
in  the  language  of  mathematics,  although  it  is  not  of  a  nature 
which  admits  of  explanation  in  a  more  elementary  and  popular 
form.  But  there  are  other  causes  affecting  the  relation  of  the 
pressure  to  the  altitude  which  must  be  taken  into  account. 
The  density  of  any  stratum  of  air  is  not  only  affected  by  the 
weight  of  the  incumbent  atmosphere,  but  also  by  the  tempera- 
ture of  the  stratum  itself.  If  any  cause  increase  this  tempera- 
ture, the  stratum  will  expand,  and  with  a  less  density  will 
support  the  same  incumbent  pressure.  If,  on  the  contrary,  any 
cause  produce  a  diminution  of  temperature,  the  stratum  will 
contract  and  acquire  a  greater  density  under  the  same  pressure. 
In  the  one  case,  therefore,  a  change  of  elevation,  which  would 
be  necessary  to  produce  a  given  change  in  the  height  of  the 
barometer  would  be  greater  than  that  computed  on  theoretical 
principles,  and  in  the  other  case  the  change  would  be  less.  The 
temperature,  therefore,  forms  an  essential  element  in  the  calcu- 
lation of  heights  by  the  barometer. 

A  rule  or  formulary  has  been  deduced,  partly  from  established 
theory,  and  partly  from  observed  effects,  by  which  the  change. 


CHAP.  IV.  ATMOSPHERIC    PRESSURE.  205 

of  elevation  may  be  deduced  from  observations  made  on  the 
barometer  and  thermometer.  To  apply  that  rule,  it  is  necessary 
to  know,  1st,  the  latitude  of  the  place  of  observation  ;  2dly,  the 
height  of  the  barometer  and  thermometer  at  the  lower  station  ; 
and,  3dly,  the  height  of  the  barometer  and  thermometer  at  the 
higher  station.  By  arithmetical  computation  the  difference  of 
the  levels  of  the  two  stations  may  then  £e  calculated.  The 
formulary  does  not  admit  of  being  explained  without  the  use  of 
mathematical  language. 

(144.)  It  has  been  already  stated,  that  the  atmospheric  pres- 
sure at  the  surface  of  the  earth  is  capable  of  supporting  a  column 
of  water  34  feet  in  height.  It  follows,  therefore,  that  if  our 
atmosphere  were  condensed  to  such  a  degree  that  its  specific 
gravity  would  be  equal  to  that  of  water,  its  height  would  be  34 
feet.  Now  the  specific  gravity  of  a  stratum  of  atmosphere  con- 
tiguous to  the  surface  is  about  840  times  less  than  the  specific 
gravity  of  water ;  that  is,  a  cubic  inch  of  water  weighs  840 
times  more  than  a  cubic  inch  of  air.  If  as  we  ascend  in  the 
atmosphere  it  continued  to  have  the  same  density,  then  its 
height  would  be  evidently  840  times  the  height  of  34  feet, 
which  would  amount  to  28,560  feet,  or  5  miles  and  a  quarter. 
It  is  obvious,  therefore,  that  since  even  at  a  small  elevation  the 
density  of  the  atmosphere  is  reduced  to  half  its  density  at  the 
surface,  the  whole  height  must  be  many  times  greater  than  this. 
The  barometer  in  the  balloon  in  which  De  Luc  ascended  fell  to 
the  height  of  12  inches.  Supposing  the  barometer  at  the  sur- 
face to  have  stood  at  that  time  at  30  inches,  it  follows  that  he 
must  have  left  three  fifths  of  the  whole  atmosphere  below  him. 
His  elevation  was  upwards  of  20,000  feet. 

(145.)  A  column  of  pure  mercury,  whose  base  is  a  square 
inch,  and  whose  height  is  30  inches,  weighs  about  15  Ibs.  avoir- 
dupois. It  follows,  therefore,  that  when  the  barometer  stands 
at  30  inches  the  atmosphere  exerts  a  pressure  on  each  square 
inch  of  the  surface  of  the  mercury  in  the  cistern  amounting  to 
15  Ibs.  Now  it  is  the  nature  of  a  fluid  to  transmit  pressure 
equally  in  every  direction ;  and  if  the  surface  on  which  the 
atmosphere  acts  were  presented  to  it  laterally,  obliquely,  or 
downwards,  still  the  pressure  would  be  the  same.  Taking, 
therefore,  the  medium  height  of  the  barometric  column  at  30 
inches,  it  follows  that  all  bodies  which  exist  at  the  surface  of 
the  earth  exposed  to  our  atmosphere  are  continually  under  this 
pressure,  and  that  every  square  inch  on  their  surface  constantly 
sustains  a  force  of  about  15  pounds.  Thus,  the  body  of  a  man, 
the  surface  of  which  amounts  to  2000  square  inches,  will  sus- 
tain a  pressure  from  the  surrounding  air  to  the  enormous  amount 
of  30,000  pounds. 

It  might  at  first  view  be  expected  that  this  great  force  to 
18 


206  A    TREATISE    ON    PNEUMATICS.  CHAP.    IV. 

which  all  bodies  are  subject  would  produce  manifest  effects,  so 
as 'to  crush,  compress,  or  break  them,  whereas  we  find  bodies 
of  most  delicate  texture  unaffected  by  it.  Thus  a  close  bag, 
made  of  the  finest  silver  paper,  and  partially  filled  with  air,  is 
apparently  subject  to  no  external  force.  Its  sides  do  not 
collapse.  This  arises  partly  from  the  circumstance  of  the  pres- 
sure on  every  side,  and  in  every  direction  being  equal,  and, 
therefore,  producing  mechanical  equilibrium.  It  is  obvious  that 
a  body  which  is  driven  in  every  possible  direction  upwards  and 
downwards,  laterally  and  obliquely,  with  equal  forces,  will  not 
move  in  any  one  direction  ;  for  to  suppose  such  a  motion  would 
be  to  assume  that  the  quantity  of  pressure  in  that  direction 
exceeds  the  quantity  of  pressure  in  other  directions.  But  still, 
though  a  body  may  not  be  driven  in  any  direction  by  the  atmos- 
pheric pressure,  it  may  happen  that  its  parts  are  crushed  and 
compressed.  We  do  not,  however,  find  this  to  happen.  This 
arises  from  the  fact,  that  the  elastic  force  of  the  air  is  equal  to 
its  pressure  ;  and  since  the  internal  cavities  of  a  body,  such  as 
the  thin  bag  above  mentioned,  are  filled  with  air,  which  is  con- 
fined within  them,  that  air  has  precisely  the  same  tendency  to 
swell  the  bag,  and  to  keep  the  parts  asunder,  as  the  external 
pressure  of  the  atmosphere  has  to  make  them  collapse. 

In  the  same  manner  we  may  account  for  the  fact  that  animals 
move  freely  in  the  air  without  being  sensible  of  the  enormous 
pressure  to  which  their  bodies  are  subject.  The  internal 
parts  of  their  bodies  are  filled  with  fluids,  both  in  the  liquid  and 
gaseous  states,  which  offer  a  pressure  from  within  exactly 
equivalent  to  the  external  pressure  of  the  air.  This  may  be 
easily  rendered  manifest  by  applying  to  the  skin  the  mouth  of 
a  close  vessel,  to  which  an  exhausting  syringe  is  attached.  By 
this  instrument,  which  will  be  described  hereafter,  the  air  may 
be  rarefied  in  the  vessel,  and  the  atmospheric  pressure  conse- 
quently partially  removed  from  the  skin.  Immediately  the 
force  of  the  fluid  from  within  will  swell  the  skin,  and  cause  it 
to  be  sucked  into  the  glass.  This  experiment  may  be  perform- 
ed by  the  mouth  on  the  flesh  of  the  hand  or  arm.  If  the  lips  be 
applied  to  the  flesh,  and  the  breath  drawn  in  so  as  to  produce  a 
partial  vacuum  in  the  mouth,  the  skin  will  be  draM'n  or  sucked 
into  the  mouth.  This  effect  is  owing,  not  to  any  force  resident 
in  the  lips  or  the  mouth  drawing  the  skin  in,  but  to  the  fact  that 
the  usual  external  pressure  is  removed,  and  that  the  pressure 
from  within  is  suffered  to  prevail. 

(146.)  All  cases  of  that  class  of  effects  which  are  commonly 
expressed  by  the  word  suction  are  accounted  for  in  the  same 
manner. 

If  a  flat  piece  of  moist  leather  be  put  in  close  contact  with  a 
heavy  body,  as  a  stone,  it  will  be  found  to  adhere  to  it  with 


CHAP.    IV.  SUCTION. — BREATHING.  207 

considerable  force,  and  if  a  cord  of  sufficient  length  be  attach- 
ed to  the  centre  of  the  leather,  the  stone  may  be  raised  by  the 
cord.  This  effect  arises  from  the  exclusion  of  the  air  between 
the  leather  and  the  stone.  The  weight  of  the  atmosphere  presses 
their  surfaces  together  with  a  force  amounting  to  15  pounds 
on  every  square  inch  of  those  surfaces  in  contact.  If  the  weight 
of  the  stone  be  less  than  the  number  of  pounds  which  would  be 
expressed  by  multiplying  the  number  of  square  inches  in  the 
surfaces  of  contact  by  15,  then  the  stone  may  be  raised  by  the 
leather  ;  but  if  the  stone  exceed  this  weight,  it  will  not  suffer 
itself  to  be  elevated  by  these  means. 

The  power  of  flies  and  other  insects  to  walk  on  ceilings  and 
surfaces  presented  downwards,  or  upon  smooth  panes  of  glass 
in  an  upright  position,  is  said  to  depend  on  the  formation  of  their 
feet.  This  is  such  that  they  act  in  the  manner  above  described 
respecting  the  leather  attached  to  a  stone  ;  the  feet,  in  fact,  act 
as  suckers,  excluding  the  air  between  them  and  the  surface 
with  which  they  are  in  contact,  and  the  atmospheric  pressure 
keeps  the  animal  in  its  position.  In  the  same  manner  the 
hydrostatic  pressure  attaches  fishes  to  rocks. 

The  pressure  and  elasticity  of  the  air  are  both  exercised  in 
the  act  of  breathing.  When  we  draw  in  the  breath  we  first 
make  an  enlarged  space  in  the  chest.  The  pressure  of  the  ex- 
ternal atmosphere  then  forces  air  into  this  space  so  as  to  fill  it. 
By  a  muscular  action  the  lungs  are  next  compressed  so  as  to 
give  this  air  a  greater  elasticity  than  the  pressure  of  the  exter- 
nal atmosphere.  By  the  excess  of  this  elasticity  it  is  propelled, 
and  escapes  by  the  mouth  and  nose.  It  is  obvious,  therefore, 
that  the  air  enters  the  lungs  not  by  any  direct  act  of  these  upon 
it,  but  by  the  weight  of  the  atmosphere  forcing  it  into  an  empty 
space,  and  that  it  is  expired  by  the  action  of  the  lungs  in  com- 
pressing it.* 

The  action  of  common  bellows  is  precisely  similar,  except 
that  the  aperture  at  which  the  air  is  draAvn  in  is  different  from 
that  at  which  it  is  expelled.  In  the  lower  board  of  the  bellows 

*  There  are  tv.-o  sets  of  cavities  concerned  in  respiration,  one  within  the  other. 
The  air  is  admitted  only  into  the  interior  cavities  or  those  of  the  lungs,  an  organ 
contained  in  the  chest.  Neglecting  the  actual  division  of  the  chest  into  two  cav- 
ities, as  well  as  the  cellular  structure  of  the  lungs,  we  may  illustrate  the  pneu- 
matic principles  of  respiration  by  considering  the  lungs  as  a  distensible  and  elastic 
bag,  and  the  chest  as  a  firm,  yet  dilatable  box,  in  which  it  is  contained,  and  by 
which  its  outer  surface  is  alternately  pressed  and  relieved  from  pressure.  There 
is  no  empty  space  in  the  lungs,  as  but  a  small  proportion  of  the  air  is  expelled  ; 
and  I  should  prefer  considering  the  elasticity  of  the  portion  which  remains,  rather 
than  the  atmospheric  pressure,  as  the  cause  whic'-i  directly  produces  the  expansion 
of  the  lungs  when  the  dilatation  of  the  chest  by  the  action  of  its  muscles  removes 
the  pressure  from  the  surface  of  the  lungs.  The  diminished  elasticity  of  the  air 
which  results  from  its  expansion,  allows  the  atmospheric  pressure  to  preponderate, 
and  force  into  the  lungs  new  portions  of  air  continually  as  long  as  they  are  dilating. 
Next,  by  a  muscular  action  of  the  chest,  assisted  by  the  elasticity  of  certain  parts, 
the  air  of  the  lungs  ia  compressed  and  partly  expelled. — AM.  ED. 


208  A  TREATISE  ON  PNEUMATICS.  CHAP.  IV. 

is  a  hole  covered  by  a  valve,  consisting  of  a  flat  piece  of  stiff 
leather,  movable  on  a  hinge,  and  which  lies  on  the  hole,  but  is 
capable  of  being  raised  by  a  slight  pressure.  When  the  upper 
board  of  the  bellows  is  raised,  the  internal  cavity  is  suddenly 
enlarged,  and  the  air  contained  in  it  is  considerably  rarefied. 
The  pressure  of  the  atmosphere  forces  in  air  at  the  nozle ; 
but  this  being  too  small  to  allow  its  admission  with  sufficient 
ease  and  speed,  the  valve  covering  the  hole  is  acted  upon  by 
the  atmosphere,  and  raised,  and  air  rushes  in  through  the  large 
aperture  under  it.  When  the  space  between  the  boards  is  filled 
with  air  in  its  common  state,  the  upper  board  is  depressed,  and 
the  air  confined  in  the  bellows  is  suddenly  condensed.  The 
valve  covering  the  hole  is  thus  kept  firmly  closed,  and  the  air 
has  no  escape  except  through  the  nozle,  from  which  it  issues 
with  a  force  proportional  to  the  pressure  exerted  on  the  upper 
board.  A  bellows,  such  as  that  in  common  domestic  use,  thus 
simply  constructed,  has  an  intermitting  action,  and  blows  by 
fits,  its  action  being  suspended  while  the  upper  board  is  being 
raised.  In  forges  and  large  factories,  in  which  fires  are  exten- 
sively used,  it  is  found  necessary  to  command  a  constant  and 
unremitting  stream  of  air,  which  may  be  conducted  through  the 
fuel  so  as  to  keep  it  in  vivid  combustion.  This  is  effected  by 
bellows  with  three  boards,  the  centre  board  being  fixed  and 
furnished  with  a  valve  opening  upwards,  the  lower  board  being 
movable  with  a  valve  also  opening  upwards,  and  the  upper  board 
being  under  a  continual  pressure  by  weights  acting  upon  it. 
When  the  lower  board  is  let  down,  so  that  the  chamber  between 
it  and  the  middle  board  is  enlarged,  the  air 'included  between 
these  boards  being  rarefied,  the  external  pressure  of  the  atmos- 
phere will  open  the  valve  in  the  lower  board,  and  the  chamber 
between  the  lower  and  middle  boards  will  be  filled  with  air  in 
its  common  state.  The  lower  board  is  now  raised  by  the  power 
which  works  the  bellows,  and  the  air  between  it  and  the  middle 
board  is  condensed.  It  cannot  escape  through  the  lower  valve, 
because  it  opens  upwards.  It  acts,  therefore,  with  a  pressure 
proportional  to  the  working  power  on  the  valve  in  the  middle 
board,  and  it  forces  open  this  valve,  which  opens  upwards.  The 
air  is  thus  driven  from  between  the  lower  and  middle  boards 
into  the  chamber  between  the  middle  and  upper  boards.  It 
cannot  return  from  this  chamber,  because  the  valve  in  the  mid- 
dle board  opens  upwards.  The  upper  board  being  loaded  with 
weights,  it  will  be  condensed  while  included  in  this  chamber, 
and  will  issue  from  the  nozle  with  a  force  proportionate  to  the 
weights.  While  the  air  is  thus  rushing  from  the  nozle,  the 
lower  board  is  let  down  and  again  drawn  up,  and  a  fresh  supply 
of  air  is  brought  into  the  chamber  between  the  upper  and  mid- 
dle board.  This  air  is  introduced  between  the  middle  and 


CHAP.  IV.  VENT-PEG. TEA-KETTLE,    &/C.  209 

upper  board  before  the  former  supply  has  been  exhausted,  and 
by  working  the  bellows  with  sufficient  speed  a  large  quantity 
of  air  will  be  collected  in  the  upper  chamber,  so  that  the  weights 
on  the  upper  board  will  force  a  continual  stream  of  air  through 
the  nozle. 

The  effect  produced  by  a  vent-peg  in  a  cask  of  liquid  depends 
on  the  atmospheric  pressure.  If  the  vent-peg  stop  the  hole  in 
the  top  while  the  liquid  is  discharged  by  the  cock  below,  a  space 
will  remain  at  the  top  of  the  barrel  in  which  the  air  originally 
confined  is  allowed  to  expand  and  become  rarefied :  its  pressure 
on  the  surface  of  the  liquid  above  will,  therefore,  be  less  than 
the  atmospheric  pressure  resisting  the  escape  of  the  liquid  at 
the  cock ;  but  still  the  weight  of  the  liquid  itself,  pressing  down- 
wards towards  the  cock,  will  cause  the  discharge  to  continue  until 
the  rarefaction  of  the  air  becomes  so  great,  that  the  excess  of  the 
atmospheric  pressure  is  more  than  sufficient  to  resist  the  escape 
of  the  liquid  ;  the  flow  from  the  cock  will  therefore  be  stopped. 
If  the  vent-peg  be  now  removed  from  the  hole,  air  will  be  heard 
to  rush  in  with  considerable  force  and  fill  the  space  above  the 
liquid.  The  atmospheric  pressure  on  the  surface  above  and  on 
the  mouth  of  the  cock  being  now  equal,  the  liquid  will  escape 
from  the  cock  by  the  effect  of  the  pressure  of  the  superior 
column,  according  to  the  principles  established  in  hydrostatics. 
If  the  vent-peg  be  again  placed  in  the  hole';  the  flow  from  the 
cock  will  be  gradually  diminished,  and  will  at  length  cease. 
Upon  the  removal  of  the  vent-peg,  the  same  effect  will  be  ob- 
served as  before. 

If  the  lid  of  a  tea-pot  be  perfectly  close,. and  fit  the  mouth 
air-tight,  or  if  the  interstices,  as  frequently  happens,  be  stopped 
by  the  liquid  which  lies  round  the  edge  of  the  mouth,  then  all 
communication  between  the  surface  of  the  liquid  in  the  vessel 
and  the  external  air  is  cut  off.  If  we  now  attempt  to  pour  liquid 
from  the  tea-pot,  it  will  flow  at  first,  but  will  immediately  cease. 
In  this  case  the  air  under  the  lid  becomes  rarefied,  and  the 
pressure  on  the  surface  of  the  liquid  in  the  tea-pot  is  so  far 
diminished,  that  the  atmospheric  pressure  resists  its  discharge 
at  the  spout. 

To  remedy  this  inconvenience,  it  is  usual  to  make  a  small  hole 
somewhere  in  the  lid  of  the  tea-pot  for  the  admission  of  air ; 
this  hole  serves  the  same  purpose  as  the  hole  for  the  vent-peg 
in  the  cask. 

Although  it  is  not  usually  practised,  a  small  hole  should  be 
made  in  the  lid  of  a  kettle,  but  for  a  different  reason.  If  the 
lid  of  a  kettle  fit  it  closely,  so  as  to  stop  all  communication  be- 
tween the  external  air  and  the  interior  of  the  vessel,  when  the 
water  contained  in  it  becomes  heated,  £team  will  rise  from  its 
surface,  and  the  air  enclosed  in  the  space  between  the  surface 
18* 


210  A    TREATISE    ON    PNEUMATICS.  CHAP.    IV. 

and  the  lid  being  heated,  will  acquire  an  increased  elastic  force. 
From  these  causes,  the  pressure  which  acts  on  the  surface  of 
the  water  in  the  kettle  will  continually  increase,  so  long  as  the 
lid  maintains  its  position :  this  pressure,  transmitted  by  the 
water  in  the  kettle,  will  overcome  the  pressure  of  the  atmos- 
phere acting  on  the  water  in  the  spout,  and  the  effect  will  be 
that  the  water  will  be  raised  in  the  spout  and  flow  from  it ;  or, 
if  the  lid  be  not  firmly  enough  fixed  to  withstand  the  pressure 
of  the  steam,  it  will  be  blown  off  the  kettle.  Such  effects  fall 
within  every  one's  experience.  If  a  small  hole  were  made  in 
the  lid  these  effects  would  be  prevented. 

Ink  bottles,  constructed  so  as  to  prevent  the  inconvenience 
of  the  ink  thickening  and  drying,  owe  their  efficacy  to  the 
atmospheric  pressure.  The  quantity  of  evaporation  which 
takes  place  in  the  liquid,  other  circumstances  being  the  same, 
is  proportional  to  the  quantity  of  surface  exposed  to  the  external 
air.  To  diminish  this  quantity  of  surface,  without  inconvenient- 
ly diminishing  the  quantity  of  ink  in  the  bottle,  bottles  have 
been  constructed  of  the  shape  represented  in/g\  18.  A  B  is  a 

Fig.  1C. 


close  glass  vessel,  from  the  bottom  of  which  a  short  tube  B 
proceeds,  from  which  another  short  tube  rises  perpendicularly. 
The  depth  of  the  tube  C  is  such  as  will  be  sufficient  for  the 
immersion  of  a  pen.  When  ink  is  poured  in  at  C,  the  bottle, 
being  placed  in  an  inclined  position,  is  gradually  filled  up  to 
the  knob  A  :  if  the  bottle  be  now  placed  in  the  position  repre- 
sented in  the  figure,  the  chamber  A  B  being  filled  with  the 
liquid,  the  air  will  be  excluded  from  it,  and  the  pressure  tend- 
ing to  force  the  ink  upwards  in  the  short  tube  C  will  be  equal 
to  the  weight  of  the  column  of  ink,  the  height  of  which  is  equal 
to  the  depth  of  the  ink  in  the  bottle  A  B,  and  the  base  of  which 
is  equal  to  the  section  of  the  tube  C.  This  will  be  manifest 
from  the  properties  of  hydrostatic  pressure  established  in  Hy- 
drostatics, chap.  iii.  Now  the  atmospheric  pressure  acts  on  the 
surface  C  with  a  force  which  would  be  capable  of  sustaining  a 
column  of  ink  many  times  the  height  of  the  bottle  A  B ;  conse- 


CHAP.  IV.  PNEUMATIC    TROUGH.  211 

quently,  this  pressure  will  effectually  resist  the  escape  of  the 
ink  from  the  mouth  C,  and  will  keep  it  suspended  in  the  bottle 
A  B.  In  this  case  the  whole  surface,  which  is  exposed  to  the 
effect  of  evaporation,  is  the  surface  of  liquid  in  the  tube  C  ; 
and,  consequently,  an  ink  bottle  of  this  kind  may  be  left  many 
months  in  a  warm  room,  and  no  perceptible  diminution  in  the 
quantity  of  ink,  or  change  in  its  quality,  will  take  place.  As 
the  ink  in  the  short  tube  C  is  consumed  by  use,  its  surface  will 
fall  to  a  level  with  the  tube  B.  A  small  bubble  of  air  will  then 
insinuate  itself  through  the  tube  B,  and  will  rise  to  the  top  of 
the  bottle  A  B ;  there  it  will  exert  an  elastic  pressure,  which 
will  cause  the  surface  in  C  to  rise  a  little  higher,  and  this  effect 
will  be  continually  repeated  until  all  the  ink  in  the  bottle  has 
been  used. 

The  only  inconvenience  which  has  been  attributed  to  these 
ink  bottles  arises  from  sudden  changes  in  the  temperature  to 
which  they  are  exposed.  When  the  external  air,  having  been 
previously  warm,  becomes  suddenly  cool,  the  small  quantity  of 
air  which  is  included  in  the  bottle  A,  not  being  cooled  BO  fast 
as  the  external  air,  will  exert  an  elastic  pressure  which  will 
cause  the  ink.  to  overflow  at  C.  This  is  an  effect,  however, 
which  we  have  never  observed,  although  we  have  seen  these 
bottles  much  used.* 

If  such  an  ink  bottle  be  placed  upon  a  marble  chimney-piece, 
or  any  other  surface  heated  beyond  the  temperature  of  the  air 
in  the  room,  the  air  confined  in  the  bottle  will  then  become 
heated,  and  acquire  increased  elastic  force,  and,  in  this  case, 
the  ink  will  overflow. 

The  fountains  for  supplying  water  to  bird  cages  are  con- 
structed upon  the  same  principle. 

The  pneumatic  trough  used  in  the  chemical  laboratory,  and 
the  gas  holders,  or  gasometers,  used  in  gas  works,  depend  on 
the  atmospheric  pressure.  A  vessel,  having  its  mouth  upwards, 
is  completely  filled  with  a  liquid.  The  mouth  is  then  stopped, 
a  flat  piece  of  glass,  or  a  smooth  plate  of  metal,  pressed  against 
it,  and  the  vessel  is  inverted,  the  mouth  being  plunged  in  a 
cistern  filled  with  the  same  liquid.  If  the  height  of  the  vessel 
in  this  case  be  less  than  the  height  of  the  column  of  the  liquid 
which  the  atmospheric  pressure  would  support,  the  vessel  will 
continue  to  be  completely  filled  with  the  liquid,  even  after  the 
plate  is  removed  from  its  mouth ;  for  the  atmospheric  pressure 
acting  on  the  surface  of  the  liquid  in  the  cistern  will  prevent 
the  liquid  contained  in  the  vessel  from  falling  out  of  it.  Any 
one  may  satisfy  himself  of  this  fact.  Take  a  wine  glass,  and 

*  If  any  inconvenience  arise,  it  would  be  from  an  increase  in  the  temperature, 
and  consequently  the  elasticity,  of  the  included  air,  or  from  a  diminution  of  tho  at- 
mospheric pressure. — AM.  ED. 


212 


A  TREATISE  OX  PNEUMATICS. 


CHAP.  IV. 


fill  it  with  water,  and  then,  having  applied  a  piece  of  card  to  its 
mouth  so  as  to  prevent  the  water  from  escaping,  invert  it,  and 
plunge  the  mouth  downwards  in  a  basin  of  water.  Let  the  card 
be  then  removed,  and  let  the  glass  be  raised  above  the  surface, 
still,  however,  keeping  the  edge  of  its  mouth  below  the  surface. 
It  will  be  observed  that  the  glass  will  still  remain  completely 
filled  with  water.  Take  a  small  quill,  or  a  hollow  piece  of 
straw,  and  insert  one  end  in  the  water,  so  that  it  will  be  imme- 
diately below  the  mouth  of  the  glass,  and  at  the  same  time 
blow  gently  through  the  other  end,  so  as  to  introduce  air  in 
small  quantities  into  the  water  immediately  under  the  mouth  of 
the  glass.  This  air  will  ascend  in  bubbles,  and  will  find  its 
way  to  the  highest  part  of  the  glass,  and,  remaining  there,  will 
expel  the  water  from  it ;  and  this  will  continue  so  long  as  air  is 
supplied,  until  all  the  water  contained  in  the  glass  is  expelled 
from  it,  and  the  glass  is  filled  with  air.  If  the  process  be  further 
continued,  tho  air  will  begin  to  escape  under  the  edge  of  the 
glass,  and  rise  in  bubbles  to  the  surface. 

The  pneumatic  trough  is  a  large  cistern  filled  with  mercury, 
in  which  is  placed,  below  the  surface  of  the  liquid,  a  shelf  to 
support  a  receiver.  By  plunging  any  vessel  in  the  deeper  part 
of  the  trough,  it  may  be  filled  with  mercury,  and  if  it  be  slowly 
raised,  keeping  its  mouth  still  below  the  surface  of  the  liquid, 
it  will  still  remain  filled  with  mercury  by  the  pressure  of  the 
atmosphere  acting  on  the  surface  of  the  mercury  in  the  trough. 
The  mouth  of  the  vessel  may  then  be  placed  on  the  shelf,  while 
the  vessel  itself  is  above  the  surface  of  the  mercury.  The 
trough  is  represented  infg.  19.  at  A  B.  The  shelf  is  placed  .in 

Fig.  19. 


it  at  C ;  a  receiver  R  is  placed  on  the  shelf,  with  its  mouth 
downwards,  over  an  aperture  D,  which  communicates  with  a 


CHAP.    IV.  NOISE    IN    DECANTING    WINE.  213 

tube,  by  which  gas  may  be  introduced.  The  gas  passing 
through  the  tube  rises  in  bubbles  through  the  mercury  in  the 
receiver,  and  lodges  at  the  top  ;  and,  by  continuing  this  process, 
the  whole  of  the  mercury  will  at  length  be  expelled  from  the 
receiver,  and  its  place  filled  with  the  gas.  In  this  manner  gases 
of  various  kinds  may  be  preserved  out  of  contact  with  the  at- 
mosphere, and  the  same  shelf  may  be  furnished  with  several 
holes,  and  may  support  a  number  of  different  jars. 

The  gasometer  used  in  gas  works  is  constructed  on  the  same 
principles,  only  on  a  different  scale.  When  used  for  great  sup- 
plies of  gas,  such  as  are  necessary  for  the  illumination  of  towns, 
these  vessels  are  constructed  of  a  very  large  size,  and  are  im- 
mersed in  pits  lined  with  cast  iron,  and  filled  with  water.  It  is 
clear  that  all  which  has  been  just  explained  will  be  equally 
applicable,  whatever  be  the  liquid  used  in  the  cistern  ;  and  for 
different  gases  it  is  necessary  to  use  different  liquids,  since  the 
contact  with  particular  liquids  will  frequently  affect  the  quality 
of  the  gas. 

The  peculiar  guggling  noise  which  is  produced  in  decanting 
wine,  arises  from  the  pressure  of  the  atmosphere  forcing  air  into 
the  interior  of  the  bottle.  In  the  first  instance,  the  neck  of  the 
bottle  is  completely  filled  with  liquid,  so  as  to  stop  the  admis- 
sion of  air.  When  a  part  of  the  wine  has  flowed  out,  and  an 
empty  space  is  formed  within  the  bottle,  the  atmospheric  pres- 
sure forces  in  a  bubble  of  air  through  the  liquid  in  the  neck, 
which,  by  rushing  suddenly  into  the  interior  of  the  bottle,  pro- 
duces the  sound  alluded  to.  This  effect  is  continually  repeated 
so  long  as  the  neck  of  the  bottle  continues  to  be  choked  with 
the  liquid.  But  as  the  contents  of  the  bottle  are  discharged, 
the  liquid,  in  flowing  out,  only  partially  fills  the  neck,  and  while 
a  stream  of  wine  passes  out  through  the  lower  half  of  the  neck, 
a  stream  of  air  passes  in  through  the  upper  part.  The  flow 
in  this  case  being  continual  and  uninterrupted,  no  sound  takes 
place. 

The  atmospheric  pressure  acting  on  the  surface  of  liquids 
maintains  air  combined  with  them  in  a  greater  or  lesser  quan- 
tity, according  to  the  nature  of  the  liquid.  If  an  open  vessel, 
containing  a  liquid,  be  placed  under  a  receiver,  and  the  air  be 
exhausted,  the  air  combined  with  the  liquid  will  be  immediately 
set  free,  and  will  be  observed  to  rise  in  bubbles  to  the  top. 
This  effect  will  be  very  perceptible  if  water  be  used,  but  still 
more  so  in  the  case  of  beer  or  ale. 

When  liquor  is  bottled,  the  air  confined  under  the  cork  is 
condensed,  and  exerts  upon  the  surface  a  pressure  greater  than 
that  of  the  atmosphere.  This  has  the  effect  of  holding  in  com- 
bination with  the  liquor  air,  which  under  the  atmospheric  pres- 
sure only  would  escape.  If  any  air  rise  from  the  liquor  after 


214  A    TREATISE    ON    PNEUMATICS.  CHAP.    V. 

being  bottled,  it  causes  a  still  greater  condensation,  and  an  in- 
creased pressure  above  its  surface. 

If  the  nature  of  the  liquor  be  such  as  to  produce  air  in  con- 
siderable quantity,  this  condensation  will  at  length  become  so 
great  as  to  force  out  the  cork  ;  or,  failing  to  do  that,  break  the 
bottle.  This  is  found  to  happen  frequently  with  beer,  ale  or 
porter.  The  corks  in  such  cases  are  tied  down  by  cord  or 
wire. 

When  the  cork  is  drawn  from  a  bottle  containing  liquor  of 
this  kind,  the  fixed  air  being  relieved  from  the  pressure  of  the 
air  which  was  condensed  under  the  cork  instantly  makes  its 
escape,  and,  rising  in  bubbles,  produces  effervescence  and  froth. 
Hence  the  head  observed  on  porter  and  similar  liquors,  and  the 
sparkling  of  champagne  or  cider. 


CHAP.  V. 

RAREFACTION  AND  CONDENSATION  OF  AIR. 

EXHAUSTING  SYRINGE. — RATE  OF  EXHAUSTION. — IMPOSSIBLE  TO  PRO- 
DUCE A  PERFECT  VACUUM. — MECHANICAL  DEFECTS. — THE  AIR  PUMP. 
— BAROMETER  GAUGE. — SYPHON  GAUGE. — VARIOUS  FORMS  OF  AIR 
PUMP. — PUMP  WITHOUT  SUCTION  VALVE. — EXPERIMENTS  WITH  AIR 
PUMP. — BLADDER  BURST  BY  ATMOSPHERIC  PRESSURE.— BLADDER 
BURST  BY  ELASTICITY  OF  AIR. — DRIED  FRUIT  INFLATED  BY  FIXED 
AIR. — FLACCID  BLADDER  SWELLS  BY  EXPANSION. — WATER  RAISED 
BY  ELASTIC  FORCE. — A  PUMP  CANNOT  ACT  IN  THE  ABSENCE  OF  AT- 
MOSPHERIC PRESSURE. — SUCTION  CEASES  WHEN  THIS  PRESSURE  IS 
REMOVED. — THE  MAGDEBURG  HEMISPHERES. — GUINEA  AND  FEATH- 
ER EXPERIMENT.— CUPPING. —  EFFERVESCING  LIQUORS. — SPARK- 
LING OF  CHAMPAGNE,  ETC. — PRESENCE  OF  AIR  NECESSARY  FOR  THE 
TRANSMISSION  OF  SOUND. — THE  CONDENSING  SYRINGE. — THE  CON- 
DENSER. 

(147.)  WHEN  a  part  of  the  air  enclosed  in  any  vessel  is  with- 
drawn, that  which  remains,  expanding  by  its  elastic  property, 
fills  the  dimensions  of  the  vessel  as  effectually  as  before.  Un- 
der these  circumstances,  however,  it  is  obvious,  that  any  given 
space  within  the  vessel  contains  a  less  quantity  of  air  than  it 
did  previously,  inasmuch  as,  while  the  whole  dimensions  of  a 
vessel  remain  the  same,  tlje  total  quantity  of  air  diffused  through 
them  is  diminished.  When  the  same  quantity  of  air  in  this 
manner  is  caused^to  expand  into  a  greater  space,  it  is  said  to  be 
rarefied. 

But  on  the  other  hand,  when  a  vessel  containing  any  quantity 
of  air  is  caused  to  receive  an  increased  quantity,  by  additional 


CHAP.    V. 


EXHAUSTING    SYRINGE. 


215 


Fig.  20. 


J\. 


air  being  forced  into  it,  then  any  given  portion  of  its  dimen- 
sions will  contain  a  proportionally  greater  quantity  of  air  than 
it  did  before  tho  additional  air  had  been  forced  in.  Under  these 
circumstances,  the  air  contained  in  the  vessel  is  said  to  be  con- 
densed, and  it  is  our  purpose  in  the  present  chapter  to  describe 
the  mechanical  instruments  by  which  these  processes  of  rare- 
faction  and  condensation  are  practically  effected. 

The  Exhausting  Syringe. 

(148.)  The  most  sirnplo  form  of  instrument  for  producing 
the  rarefaction  of  air  is  that  which  is  called  the  exhausting  syr- 
inge. In  order  to  comprehend  the  construction  and  operation 
of  this  instrument,  let  us  suppose  AB,Jig. 
2(X,  a  cylinder,  or  barrel,  furnished  with  a 
stopcock  C,  inserted  in  a  small  aperture  in 
the  bottom.  Let  the  end  of  this  tube  be 
screwed  upon  the  vessel  R,  in  which  the 
rarefaction  is  to  be  made. 

From  the  side  of  the  barrel,  near  the  bot- 
tom, let  another  tube  D  proceed,  also  fur- 
nished with  a  stopcock.  Let  us  suppose 
the  piston  P  at  the  bottom  of  the  barrel, 
both  stopcocks  being  closed.  Let  the  pis- 
ton P  be  now  drawn  from  the  bottom  to  the 
top,  as  represented  in  Jig.  21.,  this  piston 
being  supposed  to  move  air-tight  in  the 
barrel.  A  vacuum  will  remain  between 
the  piston  P  and  the  bottom  B.  If  the 
stopcock  C  be  opened,  the  air  contained  in 
the  vessel  R  will,  by  its  elastic  force,  rush 
through  the  open  stopcock  C,  and  expand 
so  as  to  fill  tho  barrel.  Thus  the  air  which 
previously  occupied  the  dimensions  of  the 
ves3el  R  has  HOAV  expanded  through  the 
dimensions  of  R  and  A  B.  Let  the  stop- 
cock C  be  now  closed,  and  the  stopcock  D 
opened,  and  let  the  piston  P  be  pressed  to  the  bottom  of  the 
barrel.  The  air  contained  in  the  barrel  will  thus  be  forced  out 
at  the  open  stopcock  D,  and  driven  into  external  atmosphere. 
Let  the  stopcock  D  be  next  closed,  and  the  piston  again  ele- 
vated, as  in  fig.  21.  A  vacuum  will  once  more  be  produced  in 
the  barrel ;  and,  on  opening  the  stopcock  C,  the  air  in  R  will 
ugain  expand  into  the  barrel,  occupying  the  extended  dimensions 
as  before.  Let  the  stopcock  C  be  again  closed,  and  the  stop- 
cock D  opened.  If  the  piston  be  pressed  to  the  bottom  of  the 
b:.rrcl  as  before,  the  air  contained  in  the  cylinder  Avill  again  be 


216 


A    TREATISE    ON    PNEUMATICS. 


CHAP.    V. 


Fig.  21. 


expelled  through  the  stopcock  D.  By  continuing  this  process, 
alternately  opening  and  closing  the  two  stopcocks,  and  elevat- 
ing and  depressing  the  piston,  a  quantity  of  air  will  rush  from 
the  vessel  R  on  each  ascent  of  the  piston, 
and  the  same  quantity  will  be  expelled 
through  the  tube  D  on  each  descent  of  the 
piston. 

It  is  evident  that  this  process  may  be  con- 
tinued so  long  as  the  air  Avhich  remains  in  R 
is  capable  of  expanding,  by  its  elasticity, 
through  the  open  tube  C  into  the  barrel 
above. 

A  slight  degree  of  attention  only  is  neces- 
sary to  perceive  that  the  quantity  of  air  ex- 
pelled from  R  at  each  ascent  of  the  piston  is 
continually  diminished  ;  and  it  will  not  be 
difficult  even  to  explain  the  exact  rate  at 
which  this  diminution  proceeds.  Let  us  sup- 
pose the  magnitude  of  the  barrel  A  B  to  have 
any  given  proportion  to  the  dimensions  of  the 
vessel  R  ;  suppose,  for  example,  that  the  di- 
mensions of  the  barrel  are  the  ninth  part  of 
those  of  the  vessel.  "When  the  piston  is  first 
raised  from  the  bottom  to  the  top,  the  air 
which  previously  occupied  the  vessel  expands 
so  as  to  occupy  the  dimensions  of  the  vessel 
and  barrel  together.  The  barrel,  therefore, 
will  contain  a  tenth  part  of  the  whole  of  the 
enclosed  air ;  for  since  the  vessel  R  contains  nine  times  as 
much  as  the  barrel,  the  vessel  and  barrel  together  contain  ten 
times  as  much  as  the  barrel.  Consequently  the  air  enclosed 
in  the  barrel  will  necessarily  be  a  tenth  of  the  whole.  On  de- 
pressing the  piston,  this  tenth  part  is  expelled  through  the  tube 
D.  On  elevating  the  piston,  the  air  remaining  in  the  vessel  R, 
which  is  nine  tenths  of  the  original  quantity,  now  expands 
through  the  vessel  and  barrel,  and,  for  the  reason  already  as- 
signed, the  barrel  will  contain  a  tenth  part  of  this  remaining  9 
tenths ;  that  is,  it  will  contain  9  hundredth  parts  of  the  original 
quantity.  On  the  second  descent  of  the  piston,  this  9  hundredth 
parts  will  be  expelled.  The  9  tenths  which  remain  in  the  cyl- 
inder after  the  first  stroke  of  the  piston,  have  now  lost  9  hun- 
dredth parts  of  the  whole ;  and,  since  9  tenths  is  the  same  as 
90  hundredths,  9  hundredths  being  deducted  from  that  leave  a 
remainder  of  81  hundredths. 

This,  therefore,  is  the  proportion  of  the  original  quantity 
which  now  remains  in  the  vessel  R.  When  the  piston  is  next 
raised,  this  portion  will  expand,  as  before,  into  the  enlarged 


CHAP.    V. 


EXHAUSTING    SVR1NGE. 


217 


space,  and  the  tenth  part  of  it  will  rise  into  the  barrel.  But  a 
tenth  part  of  81  hundredths  is  81  thousandths.  Accordingly, 
on  the  next  descent,  this  81  thousandths  will  be  expelled.  The 
81  hundredths  which  remained  in  the  vessel  R  before  this  dim 
inution  are  thus  diminished  by  81  thousandths.  This  81  hun 
dredths  are  equivalent  to  810  thousandths,  and,  therefore,  the 
quantity  remaining  in  the  vessel  R  will  be  found  by  subtracting 
81  thousandths  from  810  thousandths.  The  remainder  will, 
therefore,  be  729  thousandths,  which  will  be  the  proportion  of 
the  original  quantity  of  air  which  remains  in  the  vessel  after 
tho  third  stroke  of  the  piston.  It  will  not  be  difficult  to  continue 
this  reasoning  further,  and  to  discover  not  only  the  quantity  of 
air  expelled  at  each  successive  stroke,  but  also  the  quantity 
remaining  in  the  vessel  R ;  and  we  may,  without  difficulty, 
compute  the  following  table  : — 


Number 
of 

Strokes. 

Proportion  of  the 
original  quantity  of 
air  expelled  at  each 
stroke. 

Proportion  of  the 
original  quantity  of 
air  remaining  after 
each  stroke. 

Total  quantity  of 
air  expelled. 

1 

10 

9 
10 

i 

10 

2 

9 

Too 

81 
100 

19 

100 

3 

81 
1,000 

729 
1,000 

27J 
1,000 

4 

729 
10,000 

6,561 
10,000 

3,439 
10,000 

• 
5 

6,561 
100,000 

59,0-19 
100,000  , 

40,951 
100,000 

59,049 

531,441 

468,559 

6 

1,000,000 

1,000,000 

1,000,000 

7 

531,441 

10,000.000 

4,782,969 
10,000,000 

5,217,031 
10,000,000 

To  make  this  table  more  intelligible,  let  us  suppose  that  the 
vessel  R  contains,  in  the  first  instance,  10,000,000  grains  of  air. 
The  first  stroke  of  the  piston  expels  a  tenth  part  of  this  quanti- 
ty, that  is,  1,000,000  grains.  There  remain  in  the  vessel  R 
9,000,000  grains.  The  tenth  part  of  this  9,000,000  is  expelled 
by  the  second  stroke,  that  is,  900,000  grains  of  air.  There  now 
remain  in  the  vessel,  8,100,000  grains.  Of  this  again  a  tenth 
19 


218 


A    TREATISE    ON    PNEUMATICS. 


CHAP.    V. 


part  is  expelled  by  the  third  stroke,  that  is,  810,000  grains. 
The  quantity  remaining  in  the  receiver  will  then  be  7,290,000 
grains.  The  tenth  part  of  this  is  expelled  by  the  fourth  stroke, 
that  is,  729,000  grains,  and  there  remain  in  the  vessel  6,561,000 
grains.  The  fifth  stroke  expels  a  tenth  part  of  this,  or  656,100 
grains,  and  there  then  remain  in  the  vessel,  5,904,900  grains. 
A  tenth  part  of  this  again  is  expelled  by  the  sixth  stroke,  that 
is,  590,490  grains,  and  the  remainder  in  the  vessel  is  5,314,410 

f  rains.     A  tenth  of  this  again,  or  531,441  grains,  is  expelled 
y  the   seventh  stroke.    The  following  table  exhibits  these 
results : — 


Number 
of 
Strokes. 

Grains  expelled 
at  each  stroke. 

Grains  remaining 
under  pressure. 

Total  number  of 
grains  expelled. 

1 

1,000,000 

9,000,000 

1,000,000 

2 

900,000 

8,100,000 

1,900;000 

3 

810,000 

7,290,000 

2,710,000 

4 

729,000 

6,561,000 

3,439,000 

5 

656,100 

5,095,900 

4,095,100 

6 

590,490 

5,314,410 

4,685,599 

7 

531,441 

4,782,969 

5,217,031 

By  attending  to  the  numbers  in  the  third  column  of  the 
above  table,  it  will  be  perceived,  that  each  succeeding  number 
is  nine  tenths  of  the  preceding  one.  It  follows,  therefore,  that 
after  each  stroke  of  the  piston,  the  quantity  of  air  which  re- 
mains in  the  vessel  R  will  be  nine  tenths  of  the  quantity  which 
it  contained  before  the  stroke.  From  a  due  consideration  of 
this  circumstance,  it  will  be  perceived  that,  however  long  the 
process  of  rarefaction  be  continued,  the  vessel  R  can  never  be 
completely  exhausted  of  air ;  for,  a  determinate  quantity  being 
contained  in  it,  nine  tenths  of  this  will  remain  after  the  first 
stroke.  After  the  second  stroke,  nine  tenths  of  this  again  will 


CHAP.    V 


EXHAUSTING    SYRINGE. 


219 


remain,  and,  however  long  the  operation  be  continued,  still  a 
determinate  quantity  will  remain  after  every  succeeding  stroke 
of  the  .piston,  this  quantity  being  nine  tenths  of  what  the  vessel 
R  contained  after  the  preceding  stroke.  But  although  a  per- 
fect exhaustion  can  never  be  attained  by  these  means,  yet  if 
the  instrument  ROAV  described  could  be  constructed  as  perfect 
in  practice  as  it  is  in  theory,  there  would  be  no  limit  whatever 
to  the  degree  to  which  the  air  in  the  vessel-R  might  be  rarefied. 
Thus,  by  a  determinate  and  finite  number  of  descents  of  the 
piston,  it  might  be  reduced  in  weight  to  the  millionth  part  of  a 
grain,  or  even  to  a  quantity  millions  of  times  less  than  this. 
Still,  however  small  the  quantity  which  may  remain  in  the 
vessel  R,  so  long  as  the  elastic  force  by  which  the  particles 
repel  each  other  exceeds  the  weight  of  the  final  or  ultimate 
particles  of  the  air,  so  long  that  repulsive  energy  will  cause  it 
to  expand  through  the  tube  C  into  the  cylinder  A  B.* 

The  exhausting  syringe  used  in  practice 
differs  in  some  particulars  from  that  which  we 
have  here  described  with  a  view  to  illustrate 
the  principle  of  its  operation.  The  stopcocks 
C  and  D,  which  would  require  constant  ma- 
nipulation while  the  process  of  rarefaction  is 
going  forward,  are  dispensed  with  in  practice, 
and  the  elastic  pressure  of  the  air  itself  is 
made  to  act  upon  valves  which  serve  the  pur- 
poses of  these  cocks.  Let  A  B,  Jig.  22.,  rep- 
resent an  exhausting  syringe,  having  a  tube 
and  stopcock  C  proceeding  from  the  lower  part 
as  already  described.  The  tube  C  is  screwed 
to  a  very  small  aperture  in  the  bottom  of  the 
barrel.  Across  this  aperture  is  stretched  a 
small  piece  of  oiled  silk,  which  is  impervious 
to  air.  It  is  extended  across  the  aperture  so 
loosely,  that  a  slight  pressure  from  below  will 
produce  an  open  space  between  it  and  the  sur- 
face of  the  bottom  near  the  aperture,  capable 
of  admitting  air  from  below,  and  yet  so  tight 
that  a  pressure  from  above  will  cause  it  to  lie 
close  against  the  bottom,  round  the  aperture, 
BO  as  to  stop  the  passage  of  air  from  above. 

By  this  arrangement  it  is  possible  for  air 
pressed  with  a  sufficient  force  to  enter  the  barrel  through  the 

*  If  the  quantity  of  air  in  the  vessel  R  at  the  commencement  of  the  process 
be  expressed  by  1,  then  the  quantity  after  one  stroke  of  the  piston  will  be 
(-9?7),  after  tico  strokes  2 


2,  after  **««  strokes 


ami  after  n  stroke*! 


220 


A    TREATISE    ON    PNEUMATICS.  CHAP.    V. 


valve  V,  when  the  stopcock  C  is  opened;  but  it  is  impossible, 
the  other  hand,  for  air  pressing  above  the  valve  to  escape 
through  it,  since  the  pressure  of  the  air  only  serves  to  render 
more  close  the  contact  between  the  valve  and  the  surface  sur- 
rounding the  aperture  which  it  covers.     A  small  hole  is  pierced 
irough  the  piston,  extending  from  the  lower  to  the  upper 
surface,  and  this  hole  at  the  upper  surface  is  covered  with  an 
oiled  silk  valve  V,  in  the  same  manner  as  the  aperture  V  in  the 
bottom.     For  the  reasons  already  assigned  it  is,  therefore,  pos- 
s   tor  air  to  pass  up  through  this  hole  in  the  piston,  and 
escape  at  the  upper  surface  ;  but  it  is  impossible  for  air,  by  any 
pressure   to  pass  m  the  contrary  direction,  since  such  pressure 
only  renders  the  contact  of  the  valve  more  intimate,  and,  conse- 
quently, causes  it  to  be  more  impervious  to  air. 

Let  us  suppose  an  instrument  thus  constructed  to  be  attached 
to  a  vessel  R,  m  which  the  rarefaction  is  to  be  produced,  and 
the  stopcock  C  to  be  opened.     On  raising  the  piston  P  a  vacu- 
um will  be  produced  between  it  and  the  valve  V.     The  piston 
valve  V'  will  now  be  pressed  downwards  by  the  weight  of  the 
atmosphere,  and  will  be  subject  to  no  pressure  from  below 
ecause  of  the  absence  of  air  beneath  it.     It  will  then  stop 
ie  admission  of  air  from  above  the  aperture,  and  will  maintain 
.e  vacuum  below.     The  elastic  force  of  the  air  contained  in 
me  vessel  K  now  acting  upwards  against  the  exhausting  valve 
V  will  raise  it,  and  the  air  will  escape  through  the  space  be- 
ST^Sn'V11!?  the  surface  surrounding  the  aperture,  and  will 
the  barrel  above  ;  but  the  air  having  expanded  into  an 
Teased  space  will  have  an  elastic  force  less  than  that  of  the 
3rnal  air,  and  consequently  the  piston  valve  V'  will  be  press- 
d  down  by  a  greater  force  than  it  is  pressed  up,  and  will 
therefore  remain  closed.     Let  the  piston  be  now  depressed  :  as 
iscends  the  air  enclosed  in  the  cylinder  acquires  increased 
•  force,  and  pressing  upon  the  exhausting  valve  V  causes 
close,  so  as  to  intercept  the  air  in  the  cylinder  from  the 
I  K.     When  the  piston  has  descended  in  the  barrel  throuo-h 
icn  a  space  as  to  condense  the  air  beneath  it,  so  as  to  give  it 
a  greater  elastic  force  than  the  external  atmosphere,  it  will 
press  the  piston  valve  V  upwards,  with  a  greater  force  than 
the  external  air  presses  it  downwards.     Consequently  the  valve 
V   will  be  opened,  and  the  air  confined  beneath  the  piston  will 
begin  to  escape  through  it.     When  the  piston  has  arrived  at 
the  bottom  of  the  barrel,  the  whole  of  the  air  will  thus  be  ex- 
pelled.    This  process  is  repeated  whenever  the  piston  is  raised 
depressed ;  and  thus  the  valves,  which  in  the  form  adopted 
tor  explanation  required  constant  manipulation,  acquire  a  self- 
ctmg  property.     This  form  of  the  instrument,  which  is  that 
mmonly  used,  is  attended  with  an  obvious  limit  to  its  opera- 


CHAP.    V.  EXHAUSTING    SYRINGE.  221 

tion,  which  does  not  exist  in  the  theoretical  form  represented 
in  Jig.  20.  It  is  evident  that  the  operation  of  the  valves  depends 
upon  the  presence  of  air  of  a  certain  determinate  elastic  force 
in  the  vessel  R,  which  elastic  force  it  is  the  purpose  of  the  in- 
strument to  reduce  indefinitely.  When  the  elastic  force  of  the 
air  contained  in  R  is  so  far  diminished  that  it  is  only  equal  to 
the  force  required  to  raise  the  valve  V,  the  action  of  the  ma- 
chine must  stop,  for  any  further  diminution  would  render  the 
air  confined  in  R  unable  to  open  the  valve,  and  therefore  no 
more  air  could  pass  into  the  barrel  A  B.  This  is  a  practical 
limit  of  the  power  of  the  exhausting  syringe.  The  degree  of 
perfection  of  which  the  instrument  is  susceptible,  therefore, 
depends  upon  making  the  valve  V  offer  as  little  resistance  to 
being  raised  as  is  consistent  with  its  being  perfectly  air-tight 
when  closed. 

But  we  have  another  limit  to  the  operation  of  this  instrument, 
arising  from  the  piston  valve  V.  This  valve  is  closed  not  only 
by  its  own  tension,  but  also  by  the  weight  of  the  incumbent 
atmosphere  above  it.  When  the  piston  is  depressed,  the  air 
included  in  the  barrel  must  first  attain  a  degree  of  elastic  force 
by  condensation  equal  to  the  pressure  of  the  atmosphere,  before 
it  can  open  the  valve  V.  But  this  is  not  sufficient :  it  must 
acquire  a  further  increased  elastic  force  equal  to  the  tension  of 
the  valve  V  over  the  aperture,  in  order  to  raise  that  valve  and 
escape,  and  therefore  the  perfection  of  this  valve  also  depends 
on  having  as  little  tension  as  is  consistent  with  being  perfectly 
air-tight  from  above. 

The  efficiency  of  the  instrument  will  also  depend  upon  the 
accuracy  with  which  the  piston  fits  the  bottom  and  sides  of  the 
barrel.  When  the  piston  is  depressed  to  the  bottom,  it  is  con- 
sidered in  theory  to  be  in  absolute  contact,  so  as  to  exclude 
every  particle  of  air  from  the  space  between  it  and  the  bottom. 
But  in  practice  this  perfection  can  never  be  obtained.  It  may, 
however,  be  very  accurately  fitted,  and  the  air  retained  between 
it  and  the  bottom  may  be  reduced  almost  without  limit.  The 
small  hole  which  passes  from  the  valve  V'  to  the  bottom  of  the 
piston  will  still  remain,  however,  and  will  continue  to  be  a  re- 
ceptacle for  air,  even  when  the  piston  is  in  close  contact  with 
the  bottom.  This  space,  therefore,  produces  a  defect  in  the 
machine  which  is  not  removed.*  If  we  suppose  the  magnitude 

*  It  is  owing  to  this,  and  to  the  want  of  accuracy  in  the  mechanical  construc- 
tion of  the  piston  and  barrel,  that  the  limitatior^mentioned  in  the  preceding  para- 
graph can  exist.  However  small  the  quantity  of  air  remaining,  if  it  could  be  pent 
up  in  a  space  infinitely  small,  its  elasticity  wouJJ  overcome  the  resistance  of  the 
piston  valve  and  that  of  tho  atmospheric  pressure.  On  the  contrary,  there  is 
nothing  to  overcome  tho  resistance  of  the  exhausting  valve  but  the  enfeebled 
energy  of  rarefied  air.  This  renders  some  mechanical  _  method  of  opening  tho  ex- 
hausting valvo  mo-e  mrc^sary  to  tho  perfection  oi't'ie  instrument. — AM.  ED. 


A    TREATISE    ON    PNEUMATICS.  CHAP.    V. 

of  this  hole,  together  with  whatever  space  may  remain  unfilled 

between  the  lower  surface  of  the  piston  and  the  bottom  of  the 

barrel  to  be  the  ten  thousandth  part  of  a  solid  inch,  then  the 

valve  V'  will  cease  to  act  when  the  air  which  fills  the  barrel 

e  piston  being  at  the  top,  is  such  that,  if  condensed  into  the 

thousandth  part  of  an  inch,  its  elastic  force  will  exceed  the 

atmospheric  pressure  by  a  quantity  less  than  the  force  required 

to  open  the  valve  V'. 

This  source  of  imperfection  will  evidently  be  diminished  by 

diminishing  the  depth  of  the  aperture  below  the  valve  V  and 

by  increasing  the  size  of  the  cylinder ;  for  if  the  air  in  the'bar- 

i  be  as  many  times  rarer  than  the  external  atmosphere,  as  the 

magnitude  of  the  barrel  is  greater  than  the  magnitude  of  the 

space  below  the  valve  V,  then  this  air,  when  condensed  into 

that  space,  will  exert  a  pressure  equal  to  that  of  the  atmos- 

here.     Suppose  the  barrel  contains  ten  cubic  inches  ~of  air 

nd  that  the  magnitude  of  the  hole  is  the  hundredth  part  of  a 

cubic  inch,  then  the  magnitude  of  the  cylinder  will  be  1000  times 

the  magnitude  of  the  space  which  remains  between  the  valve 

and  the  bottom  of  the  barrel,  when  the  piston  is  pressed 

)  the  bottom.     Consequently  the  process  of  rarefaction  would 

deduced  until  the  air  in  the  receiver  would  be  rendered  1000 

times  rarer  than  the  external  atmosphere. 

The  vessel  R  being  connected  with  a  tube  furnished  with  a 

stopcock  C  may  be  detached  from  the  syringe  together  with  the 

stopcock  by  unscrewing  the  tube  C  ;  and  if  the  stopcock  be 

mously  closed,  the  interior  of  the  vessel  will  continue  to 

contain  the  rarefied  air. 

In  various  branches  of  physical  science  inquiries  continually 

arise  respecting  qualities  and  effects , of  material  substances, 

which  are  subject  to  considerable  modification  by  the  pressure 

or  other  qualities  of  the  air  which  surrounds  them  ;  and  it  is 

ten  necessary  m  such  investigations  to  discover  what  these 

qualities  and  effects  may  be,  if  the  substances  were  not  exposed 

te  mechanical  pressure  or  other  effects  consequent  upon  the 

resence  of  the  atmosphere.     Although  we  do  not  possess  any 

means  of  removing  altogether  the  presence  of  this  fluid,  yet 

rom  what  has  been  already  stated  it  is  plain  that  it  may  be  so 

attenuated  m  an  enclosed  chamber,  such  as  the  vessel  R,  that 

these  effects  may  be  diminished  in  intensity  to  any  degree 

which  experimental  inquiry  may  demand. 

With  these  views  it  is  necessary,  however,  not  only  to  be 
to  introduce  the  substances  which  are  submitted  to  exper- 
imental investigation  into  the  chamber  in  which  the  rarefaction 
3  been  accomplished,  but  also  to  be  able  to  observe  them 
when  so  situated.     The  latter  purpose  could  be  accomplished 
by  constructing  the  receptacle  R  of  ghss  ;  but  still  it  would  be 


CHAP.  V. 


AIR    PUMP. 


223 


necessary  to  have  access  to  the  interior,  and  to  construct  it  of  a 
convenient  form  to  receive  the  subjects  of  experiment,  and  even 
in  many  cases  to  be  able  to  manipulate  or  produce  changes  of 
position  on  the  object  thus  enclosed. 

For  these  purposes  the  form  of  the  vessel  R,  and  the  mode 
of  connecting  it  with  the  syringe,  must  be  somewhat  changed, 
and  the  arrangement  which  is  given  in  order  to  adapt  them 
thus  to  all  the  exigencies  of  experimental  investigation  is  called 
THE  AIR  PUMP,  an  instrument  which  we  will  now  proceed  to 
explain. 

The  Air  Pump. 

(149.)  The  vessel  in  which  the  rarefaction  is  produced  by  an 
air  pump  is  called  a  Receiver,  and  is  usually  constructed  of  glass, 
in  a  cylindrical  form,  with  an  arched  or  round  top,  furnished 
with  a  ball  as  a  convenient  handle.  A  section  R  of  this  is  rep- 
resented in  Jig.  23.  The  mouth  or  lower  part  is  open,  and  it  is 

Fig.  23. 


ground  to  a  perfectly  smooth  and  flat  edge.  A  circular  brass 
plate  is  constructed,  also  ground  truly  plane  and  perfectly 
smooth,  and  its  magnitude  is  accommodated  to  the  size  of  the 
largest  receiver  intended  to  be  used ;  a  section  of  this  plate  is 
represented  at  S  S. 

When  the  receiver  is  placed  on  the  plate  with  its  mouth 
downwards,  the  edge  of  the  mouth  and  the  surface  of  the  plate 
should  be  so  truly  plane  and  smooth,  that  they  may  rest  in  air- 
tight contact.  This  may  always  be  insured  by  smearing  the 


224  A    TREATISE    CX    PNEUMATICS.  CHAP.  V 

ground  edge  of  the  receiver  with  a  little  lard  or  unctuous  mat- 
ter. Wheji  the  receiver  is  thus  laid  on  the  plate  it  becomes 
an  enclosed  chamber,  similar  to  R,  Jig.  22.,  but  with  this  con- 
venience, that  any  substance  or  object  to  be  submitted  to 
experiment  may  be  previously  placed  under  it,  and  observed 
through  it  after  the  air  has  been  rarefied.  In  the  centre  of  the 
plate  S  S  a  small  aperture  O  communicates  with  a  tube  T, 
analogous  to  the  tube  inserted  in  the  bottom  of  the  syringe  in 
fg.  22.  This  tube  is  furnished  with  a  stopcock  at  C,  which 
when  closed  cuts  off  all  communication  between  the  receiver 
and  the  syringe,  and  -when  open  allows  the  syringe  to  act  en 
the  receiver  as  already  described. 

The  syringe  B  furnished  with  a  piston  P  is  fixed  on  a  firm 
stand,  and  the  tube  T  is  carried  in  such  a  direction  as  to  open 
a  communication  with  the  valve  V  in  the  bottom  of  the  syringe. 
To  facilitate  the  operation,  it  is  usual  to  raise  and  depress  the 
piston,  not  by  the  hand  applied  at  the  extremity  of  the  piston 
rod  as  formerly  described,  but  by  a  winch  D,  which  turns  a  toothed 
wheel  W,  working  in  corresponding  teeth,  formed  on  the  edge 
cf  the  piston  rod  E. 

It  is  not  necessary  again  to  describe  the  operation  of  the 
syringe,  since  it  is  exactly  what  has  been  already  explained 
with  reference  to  Jig.  22.  The  piston  P  is  elevated  and 
depressed  by  alternately  turning  the  wheel  W  in  opposite 
directions,  and  the  piston  valve  \T/  and  the  exhausting  valve  V 
have  the  property  and  work  in  the  manner  already  described. 
This  instrument  and  that  represented  in  fig.  22.  differ  in  noth- 
ing except  the  length  and  shape  of  the  communicating  tube  T, 
the  shape  of  the  receiver  R,  and  the  mechanical  method  of 
working  the  piston. 

To  expedite  the  process  of  rarefaction,  it  is  usual  to  provide 
two  syringes  worked  by  the  same  wheel  as  represented  in  the 
figure,  each  being  drawn  up  while  the  other  is  depressed.  By 
these  means  a  given  degree  of  rarefaction  is  produced  in  half 
the  time  which  would  be  required  with  a  single  syringe. 

In  using  this  instrument  it  is  always  desirable,  and  frequently 
necessary,  to  ascertain  the  degree  of  rarefaction  whicli  has  oeen 
accomplished  within  the  receiver.  This  is  indicated,  with  great 
precision,  by  an  apparatus  called  a  barometric  gauge,  repre- 
sented at  H  G.  This  consists  of  a  glass  tube  II  G,  the  upper 
end  H  of  which  has  free  communication  with  the  receiver  or 
rather  with  the  tube  T  at  some  point  above  the  stopcock  C. 
The"  tube  H  G  is  more  than  30  inches  in  length,  and  its  lower 
extremity  is  plunged  in  a  small  cistern  of  mercury.  As  the 
rarefaction  proceeds  in  tho  receiver,  the  elastic  force  of  the  air 
pressing  upon  the  mercury  in  the  tube  H  G  is  diminished,  and 
immediately  becomes  less  than  the  pressure  of  the  external 


CHAP.    V. 


SIPHON    GAUGE. 


225 


atmosphere  on  the  surface  of  the  mercury  in  the  cistern  M ; 
consequently  this  external  pressure  prevails,  and  forces  mercury 
up  to  a  certain  height  in  the  tube  G  H.  As  the  rarefaction  of 
the  air  in  the  receiver  increases,  its  elastic  force  being  dimin- 
ished, the  atmospheric  pressure  will  prevail  with  increased  effect, 
and  will  cause  the  column  sustained  in  the  tube  to  rise.  The 
weight  of  this  column,  combined  with  the  elastic  pressure  of 
the  air  remaining  in  the  receiver,  is  equal  to  the  atmospheric 
pressure,  because  they  are  balanced  by  it,  and  it  is  therefore 
apparent  that  the  elastic  pressure  of  the  air  in  the  receiver  must 
be  equal  to  the  excess  of  the  atmospheric  pressure  above  the 
weight  of  the  mercurial  column  in  the  tube.  Let  us  suppose 
that  the  common  barometer  stands  at  30  inches,  and  that  the 
column  in  the  gauge  measures  27  inches,  the  difference  between 
these,  namely,  3  inches  of  mercury,  will  express  the  elastic 
force  of  the  rarefied  air  in  the  receiver  ;  for  the  column  of  30 
inches  in  the  barometer  measures  the  atmospheric  pressure,  and 
the  column  of  27  inches  in  the  gauge  must  be  added  to  the 
pressure  of  the  rarefied  air,  in  order  to  obtain  the  force  which 
balances  this  pressure  ;  therefore  the  force  of  the  rarefied  air 
must  be  equivalent  to  the  pressure  of  3  inches,  by  which  the 
barometric  column  exceeds  the  mercurial  column  suspended  in 
the  gauge. 

In  small  pumps,  which  are  used  on  the  table,  gauges  of  this 
form  are  rejected  in  consequence  of  their  inconvenient  dimen- 
sions. An  instrument  called  a  siphon  gauge  is  then  used,  the 
principle  of  which  is  easily  understood.  A  small  glass  tube,  of 
8  or  10  inches  in  length,  is  bent  into  the  form  A  B  C  D,  repre- 
sented in  Jig.  24.  The  extremity  A  is  closed,  and 
the  extremity  D  opened  and  furnished  with  a 
screw,  by  which  it  may  be  attached  to  a  tube  con- 
nected with  the  tube  T,  Jig.  23.,  above  the  stop- 
cock C.  Pure  mercury  is  poured  into  the  tube 
A  B  C  D,  Jig.  24.,  until  the  leg  A  B  is  completely 
filled,  and  the  mercury  rises  to  S  about  half  an 
inch  above  the  inflection  B.  The  pressure  of  the 
atmosphere  communicating  freely  with  the  sur- 
face S  through  D  C  will  maintain  the  mercury  in 
the  space  S  B  A,  and  will  prevent  the  surface  S 
from  rising  towards  C  by  the  pressure  of  the  column 
B  A.  When  D  is  screwed  to  the  pump,  and  put 
in  communication  with  the  exhausting  tube  T,  Jig. 
23.,  above  the  stopcock  C,  then  the  surface  S  will 
be  pressed  by  the  elastic  force  of  the  air  in  the  receiver  R, 
with  which  it  communicates.  So  long  as  that  elastic  force  is 
capable  of  sustaining  the  column  of  mercury  in  the  leg  B  above 
the  level  of  the  surface  S,  this  instrument  will  give  no  indica- 


Fig.  24. 


220       .  A    TREATISE    ON    PNEUMATICS.  CHAP.  V 

tion  of  the  degree  of  rarefaction  ;  but  when,  by  the  operation 
of  the  syringe,  the  air  in  the  receiver  is  so  far  exhausted  that 
its  elastic  force  is  unable  to  sustain  the  mercurial  column  in 
B  A  above  the  level  S,  then  the  mercury  will  begin  to  fall  in 
the  leg  B  A,  and  the  surface  S  will  rise  in  the  leg  B  C.  The 
column  suspended  in  the  leg  B  A,  above  the  level  S,  will  now 
be  the  exact  measure  of  the  elastic  force  of  the  air  in  the 
receiver  which  sustains  it.  In  this  respect  the  siphon  gauge 
must  be  regarded  as  a  more  direct  measure  of  the  elastic  force 
of  the  air  in  the  receiver  than  the  barometer  gauge.  The  lat- 
ter, in  fact,  measures,  not  the  elastic  force  of  the  air  in  the 
receiver,  but  the  difference  between  that  elastic  force  and  the 
pressure  of  the  atmosphere.  To  obtain  the  elastic  force  of  the 
air  in  the  receiver  it  is  necessary  also  to  ascertain  the  indica- 
tions of  the  barometer.  The  siphon  gauge,  however,  gives  at 
once  the  pressure  of  the  air  in  the  receiver. 

(150.)  The  air  pump  has  been  constructed  from  time  to  time 
in  a  great  variety  of  forms,  the  details  of  which  it  would  not  be 
proper  to  introduce  into  the  present  treatise.  The  general 
principle  in  all  is  the  same :  they  differ  from  each  other  chiefly 
in  the  construction  of  the  piston  and  valves. 

In  the  form  which  has  been  above  described,  the  air  effects 
its  escape  from  the  receiver  at  each  stroke  of  the  piston  by 
opening  the  suction  valve  V,  fg.  23.  Now  in  whatever  way 
this  valve  is  constructed  it  must  require  some  determinate  force 
to  raise  it ;  and  this  force,  in  the  case  already  described,  is  the 
elastic  force  of  the  rarefied  air  remaining  in  the  receiver.  Thus 
the  operation  of  the  machine  is  accomplished  by  the  presence 
in  the  receiver  of  the  very  agent  which  it  is  the  object  of  the 
machine  itself  to  remove,  and  from  the  very  construction  of  the 
instrument  it  must  cease  to  act  while  yet  air  of  a  determinate 
pressure  remains  in  the  receiver. 

This  defect  has  been  sometimes  attempted  to  be  removed  by 
causing  the  suction  valve  to  open,  not  by  the  pressure  of  the 
rarefied  air,  but  by  some  mechanical  means  acted  upon  by  the 
piston.  Such  contrivances,  however,  are  found  to  be  attended 
with  peculiar  inconveniences  which  more  than  outweigh  their 
advantages.  Probably  the  most  simple  and  the  best  contrivance 
is  one  in  which  the  suction  valve  is  altogether  dispensed  with, 
and  the  air  passes  freely  through  the  open  tubes  from  the 
receiver  to  the  pump  barrel.  Let  T,fg.  25.,  be  the  exhausting 
tube  which  is  carried  from  the  receiver,  and  enters  the  pump 
barrel  at  a  point  distant  from  the  bottom  of  the  barrel  by  a  space 
equal  to  the  thickness  of  the  piston.  The  piston  P  is  a  solid 
plug,  which  moves  air-tight  in  the  barrel,  and  is  propelled  by  a 
polished  cylindrical  rod  which  slides  in  an  air-tight  collar  C  in 
the  top  of  the  cylinder,  which  in  this  case  is  closed.  A  valve  is 


;HAP.  v.  AIR  PUMP.  227 

placed  in  the  top  of  the  cylinder,  which  opens  outwards,  and 
which  may  be  constructed  in  the  same  manner  as  the  silk  valves 
already  described.  When  the  piston  descends,  it  leaves  a 
vacuum  above  it,  the  external  air  not  being  allowed  admission 

Fig.  25 


through  the  valve  at  the  top  ;  and  when  the  piston  arrives  at 
the  bottom  of  the  barrel,  it  has  passed  the  mouth  of  the  exhaust- 
ing tube  T,  and  fills  the  space  below  it.  The  air  in  the  receiver 
then  expands  into  the  empty  pump  barrel,  and  when  the  piston 
is  raised,  having  passed  the  mouth  of  the  tube  T,  the  air  which 
has  expanded  into  the  barrel  is  confined  between  the  piston  and 
the  top,  where,  as  the  piston  rises,  it  is  condensed.  When  it 
acquires  sufficient  elastic  force,  it  opens  the  valve  at  the  top, 
and  is  discharged  into  the  atmosphere. 

The  valve  in  the  top  of  the  barrel  is  in  this  case  continually 
under  the  atmospheric  pressure,  and  therefore  the  air  confined 
in  the  pump  can  never  be  driven  through  it,  until  it  is  condensed 
b .  the  piston,  so  that  its  force  shall  be  greater  than  that  of  the 
r  mosphere.  From  the  causes  already  explained,  arising  from 
inaccuracy  of  mechanical  construction,  some  small  space  must 
inevitably  remain  between  the  piston  and  the  top  of  the  barrel, 
even  when  the  piston  is  drawn  upwards  as  far  as  possible.  This 
small  space  will  contain  condensed  air,  and  the  valve  at  C  will 
cease  to  act,  when  the  air  which  occupies  this  space  exceeds 
the  atmospheric  pressure  by  a  force  less  than  the  tension  of  the 
valve. 

When  the  piston  is  pressed  to  the  bottom,  a  small  space  will 


228  A   TREATISE    ON    PNEUMATICS.  CHAP.  V. 

likewise  remain  between  the  piston  and  the  bottom,  which  will 
be  occupied  by  air,  but  at  each  ascent  of  the  piston  this  air  ex- 
pands, and  is  subject  to  constant  diminution  as  the  working  of 
the  pump  is  continued. 

The  principal  source  of  imperfection  in  such  an  instrument, 
independently  of  that  which  arises  from  the  mechanical  inac- 
curacy of  its  construction,  depends  on  the  tension  of  the  valve 
in  the  top,  and  the  pressure  of  the  atmosphere  upon  it.  To 
diminish  this  imperfection,  the  valve  in  the  top  is  sometimes 
made  to  communicate  by  a  pipe  with  a  small  subsidiary  ex- 
hausting syringe,  by  which  the  pressure  of  the  atmosphere  on 
the  valve  may  be  partially  withdrawn,  so  that  a  less  force  acting 
under  the  valve  may  open  it. 

A  perspective  view  of  an  air  pump,  with  all  its  accompani- 
ments, constructed  upon  this  principle,  is  exhibited  in  Jig.  26., 
where  the  several  parts  of  the  machine  are  marked  with  the 
same  letters  as  the  corresponding  part  in  the  sectional  diagram, 
Jig.  23.  The  subsidiary  syringe  just  alluded  to  is  also  repre- 
sented at  Q,.  It  is  worked  by  a  handle  H. 

Experiments  with  the  Air  Pump. 

(151.)  The  pressure  and  elasticity  of  air  are  capable  of  being 
strikingly  illustrated  in  various  ways  by  experiments  with  the 
air  pump. 

If  a  glass  receiver,  open  at  both  ends,  have  a  strong  bladder 
tied  upon  one  end,  so  as  to  be  air-tight,  and  be  placed  upon  the 
open  end  on  the  plate  of  an  air  pump,  when  the  air  is  exhausted 
from  the  receiver,  the  pressure  of  the  external  atmosphere  on 
the  bladder  will  immediately  cause  its  upper  surface  to  be  con- 
cave, and  when  the  air  is  sufficiently  rarefied  within  the  receiver, 
the  pressure  on  the  bladder  will  burst  it,  producing  a  loud  noise 
like  the  discharge  of  a  pistol. 

Again,  if  a  large  glass  bowl,  having  a  bladder  tied  firmly  on 
its  mouth  so  as  to  be  perfectly  air-tight,  be  pkced  under  the 
receiver  of  the  air  pump,  on  withdrawing  the  air,  the  elastic 
force  of  the  air  confined  in  the  bowl  being  still  undiminished, 
and  being  no  longer  balanced  by  the  atmospheric  pressure  on 
the  outside,  the  bladder  will  be  blown  into  a  convex  form  ;  and 
when  the  air  in  the  receiver  is  so  rarefied  that  the  elasticity  of 
the  air  confined  in  the  bowl  suffers  little  resistance,  the  bladder 
will  burst,  and  the  air  confined  in  the  bowl  will  expand  through 
the  receiver. 

(152.)  Fruit  when  dried  and  shriveled  contains  within  it  par- 
ticles of  air,  which  are  held  in  its  pores  by  the  pressure  of  the 
external  atmosphere.  If,  therefore,  this  pressure  be  removed, 
we  may  expect  that  the  air  thus  confined  will  expand,  and  if 


CHAP.  V.  EXPERIMENTS    ON   AIR. 

Fig.M. 


229 


there  is  no  aperture  in  the  skin  of  the  fruit  for  its  escape,  it  will 
distend  the  skin.  Fruit  in  this  case  placed  under  a  receiver 
will  assume  the  appearance  of  ripeness  by  exhausting  the  air ; 
for  the  expansion  of  the  air  contained  in  the  fruit,  by  inflating 
the  skin,  will  give  it  a  fresh,  ripe  appearance.  Thus  a  shriveled 
apple  will  appear  to  grow  suddenly  ripe  and  fresh  ;  and  a  bunch 
of  raisins  will  be  converted  into  a  bunch  of  ripe  grapes. 

(153.)  A  flaccid  bladder  closed  so  as  to  be  air-tight  at  the 
mouth  contains  within  it  a  small  portion  of  air.  This  air  presses, 
by  its  elasticity,  on  the  inner  surface,  which  is  resisted  by 
the  atmospheric  pressure  from  without.  If  such  a  bladder  be 
placed  under  the  receiver  of  a  pump,  and  the  air  exhausted,  the 
external  pressure  being  thus  removed,  the  elasticity  of  the  air 
included  will  cause  the  bladder  to  swell,  and  it  will  take  all  the 
20 


230 


A    TREATISE    ON    PNEUMATICS. 


CHAP.    V. 


appearance  of  being  fully  inflated.  Such  a  bladder  placed 
under  several  heavy  weights  will  raise  them 
by  the  expansion  of  the  air. 

(154.)  Let  a  close  glass  vessel  A  B,/g-.  27. 
be  partially  filled  with  water,  and  let  the  tube 
C  D  be  inserted  through  its  neck,  the  end  D 
being  below  the  surface  of  the  water ;  the  air 
above  the  surface  will  thus  be  confined.  If 
such  a  vessel  be  placed  under  a  receiver,  and 
the  air  be  withdrawn,  t^e  elastic  force  of  the 
air  confined  in  A  B  above  the  surface  of  the 
water  will  press  the  water  up  in  the  tube  D  C, 
from  which  it  will  issue  in  a  stream  at  C,  when 
the  pressure  of  the  atmosphere  is  sufficiently 
removed  by  rarefaction. 

(155.)  By  means  of  an  air  pump  we  are 
enabled  to  demonstrate  that  the  power  which 
causes  water  to  follow  the  piston  in  a  pump 
is  the  atmospheric  pressure,  by  showing  that  the 
water  will  not  follow  the  piston  when  that  atmospheric  pressure 
ia  removed.  Let  a  small  exhausting  syringe,  with  its  lower 
end  in  a  vessel  of  water,  be  placed  on  the  plate  of  the  air  pump, 
and  let  a  glass  receiver,  open  at  the  top,  be  placed  over  it.  On 
the  top  of  this  receiver  let  a  brass  cap  fitting  it  air-tight  be 
placed,  through  a  hole  in  the  centre  of  which  a  metal  rod  ter- 
minating in  a  hook  passes  air-tight.  Let  the  hook  be  attached 
to  the  end  of  the  piston  rod,  so  that  by  drawing  the  rod  up 
through  the  air-tight  collar,  the  piston  may  be  drawn  from  the 
bottom  of  the  cylinder  towards  the  top.  If  this  be  done  before 
the  air  has  been  exhausted  from  the  receiver,  the  water  will  be 
found  to  rise  after  the  piston  as  in  the  common  pump  ;  but  as 
soon  as  the  air  in  the  receiver  has  been  highly  rarefied,  it  will 
be  found  that  although  the  piston  may  be  drawn  up  in  the 
syringe  the  water  will  not  follow  it.  This  effect  may  be  ren- 
dered visible  by  constructing  the  barrel  of  the  pump  or  syringe 
of  glass,  through  which  the  water  will  be  seen  to  rise  in  the  one 
case  and  not  in  the  other. 

(156.)  If  an  air-tight  piston  be  placed  in  close  contact  with 
the  bottom  of  a  syringe  not  furnished  with  a  valve,  any  attempt 
to  draw  it  up  will  be  resisted  by  the  atmospheric  pressure  ;  and 
if  it  be  forced  to  the  top  of  the  cylinder  and  there  discharged, 
it  will  be  immediately  urged  with  considerable  force  to  the  bot- 
tom. The  atmospheric  pressure  above  the  piston,  acting  with 
a  force  of  about  15  pounds  on  the  square  inch,  produces  this 
effect ;  for  the  space  between  the  piston  and  the  bottom  of  the 
cylinder  not  containing  a»y  air,  this  pressure  is  unresisted. 
Now  if  this  piston  be  introduced  under  the  receiver  of  an  air 


CHAP.    V. 


EXPERIMENTS    ON    AIR. 


231 


Fig.  28. 


pump,  and  be  drawn  up  as  already  described,  it  will  be  found 
that  in  proportion  as  the  air  is  withdrawn  from  the  receiver, 
less  and  less  force  will  be  required  to  produce  the  effect ;  and, 
at  length,  the  rarefaction  will  become  so  great,  that  the  pres- 
sure of  the  remaining  air  is  incapable  of  overcoming  the  friction 
of  the  piston  with  the  cylinder,  and  it  will,  when  drawn  to  the 
top,  remain  there,  without  returning  to  the  bottom.  In  this 
state,  let  the  air  be  re-admitted  to  the  receiver  ;  the  piston  will 
then  be  immediately  pressed  to  the  bottom  of  the  cylinder. 

(157.)  The  celebrated  experiment  of  the  Magdeburgh  hem- 
ispheres may  be  performed  by  means  of  an  air  pump.  Two 
hollow  hemispheres,  constructed  of  brass,  as 
represented  in  fig.  28.,  are  so  formed  that 
when  placed  mouth  to  mouth  they  shall  be 
in  air-tight  contact.  They  are  furnished 
with  handles,  one  of  which  may  be  screwed 
off.  In  the  neck  to  which  this  handle  is 
screwed  is  a  tube  furnished  with  a  stopcock. 
The  handle  being  screwed  off,  let  the  hem- 
isphere be  screwed  on  the  pump  plate,  and 
the  other  hemisphere  being  placed  over  it, 
let  the  stopcock  be  opened  so  as  to  leave  a 
free  communication  between  the  interior  of. 
the  sphere  and  the  exhausting  tube  of  the  air 
pump.  The  pump  being  now  worked,  the 
interior  of  the  sphere  will  form  the  receiver 
from  which  all  communication  with  the  ex- 
ternal air  is  cut  off,  and  rarefaction  will  be 
produced  in  it  to  any  degree  which  may  be 
desired.  This  being  effected,  let  the  stop- 
cock be  closed  ;  and  let  the  sphere  be  detached  from  the  pump 
plate,  and  the  handle  screwed  upon  it.  If  then  the  two  handles 
be  drawn  in  opposite  directions,  so  as  to  pull  the  hemispheres 
from  one  another,  it  will  be  found  that  they  will  resist  with 
considerable  force.  If  the  diameter  of  the  sphere  be  6  inches, 
its  section  through  the  centre  will  be  about  28  square  inches. 
The  hemispheres  will  be  pressed  together  by  a  force  amounting 
to  15  pounds  for  every  square  inch  in  the  section.  If  28  be 
multiplied  by  15,  we  shall  obtain  420,  which  is  the  amount  of 
the  force  wi1»  which  the  hemispheres  will  be  held  together. 
If  one  of  the  handles  be  placed  on  a  strong  hook,  and  a  weight 
of  400  pounds  be  suspended  from  the  other,  the  weight  will  be 
supported  by  the  pressure  of  the  atmosphere. 

This  was  one  of  the  earliest  experiments  in  which  the  effects 
of  atmospheric  pressure  were  exhibited.  Otto  Guericke,  the 
inventor  of  the  air  pu""np,  constructed  in  1654,  a  pair  of  such 
hemispheres  one  f.-ct  in  diameter.  The  section  through  the 


232 


A    TREATISE    ON    PNEUMATICS. 


CHAP.    V. 


Fig.  29. 


centre  of  these  was  about  113  square  inches,  which,  multiplied 
by  15,  gjves  a  pressure  amounting  to  about  1700  pounds.  If 
the  exhaustion  were  complete,  the  hemispheres  would  be  held 
together  by  this  force  ;  but,  even  though  incomplete,  they  were 
still  able  to  resist  a  prodigious  force  tending  to  draw  them 
asunder.  j 

(158.)  It  is  a  consequence  of  the  general  theory  of  gravita- 
tion, that  under  the  same  circumstances,  bodies  are  attracted 
in  proportion  to  their  mass  ;  and  hence  it  would  follow,  that  all 
bodies,  whatever  be  their  masses,  should  fall  at  the  same  rate. 
Now  the  instances  which  most  commonly  come  under  our  ob- 
servation seem  to  contradict  this  inference  ;  for  we  find  a  piece 
of  metal  and  a  piece  of  paper  fall  at  very  different  rates,  and 
still  more  different  is  the  rate  at  which  a  piece  of  metal  and  a 
feather  would  fall.  The  cause  of  this  circumstance,  however, 
is  easily  explained.  The  resistance  offered  by  the  air  is  pro- 
portional to  the  quantity  of  surface  which  the  body  presents  in 
the  direction  of  its  motion.  Now  the  metal  may  present  a 
considerably  less  surface  than  the  feather,  while  the  force 
which  it  exerts  to  overcome  the  resist- 
ance is  many  times  greater,  because  of , 
its  greater  weight.  Hence  it  follows,  that 
the  resistance  of  the  air  produces  a  differ- 
ent effect  on  the  metal  compared  with  the 
effect  which  it  produces  on  the  feather  ; 
but  all  doubt  will  be  removed  if  the  feath- 
er and  the  metal  are  allowed  to  fall  in  a 
chamber  from  which  the  air  has  been 
withdrawn.  A  glass  receiver  is  repre- 
sented in  Jig.  29.,  which  may  be  placed 
on  the  plate  of  an  air  pump,  and  on  the 
top  is  placed  a  brass  cover,  which  is  air- 
tight. Under  this  several  brass  stages 
are  attached,  constructed  in  the  manner  of 
trap  doors  on  the  hinges,  and  supported  by 
small  pins,  which  project  from  the  sides 
of  a  metal  rod,  passing  through  an  air- 
tight collar  in  the  brass  cover.  By  turn- 
ing this  metal  rod  the  pins  may  be 
removed  from  under  the  trap  doors,  and 
they  will  fall,  disengaging  whatever  may 
be  placed  upon  them.  Suppose  a  piece 
of  coin  and  a  feather  be  placed  upon  one 
of  these  stages,  supported  by  a  projecting 
pin.  This  arrangement  being  made,  let 
the  brass  cover  be  placed  on  the  receiver,  so  as  to  be  air-tight, 
and  let  the  receiver  be  then  exhausted  by  the  pump.  When  a 


CHAP.  V.         PRODUCTION  OF  SOUND.  233 

high  degree  of  rarefaction  has  been  produced,  let  the  rod  be 
turned  by  the  handle  at  the  top,  so  as  to  remove  the  pin  from 
under  the  stage  ;  the  coin  and  the  feather  will  be  immediately 
let  fall,  and  it  will  be  observed  that  they  will  both  descend  at 
exactly  the  same  rate,  and  strike  the  bottom  at  the  same  in- 
stant. This  is  the  experiment  commonly  known  by  the  name 
of  "  the  guinea  and  feather  experiment." 

(159.)  The  surgical  process  called  cupping,  consists  in  re- 
moving the  atmospheric  pressure  from  the  part  of  the  body 
submitted  to  the  operation.  A  vessel  with  an  open  mouth  is 
connected  with  an  exhausting  syringe.  The  mouth  is  applied 
in  air-tight  contact  with  the  skin,  and,  by  working  the  syringe, 
14  part  of  the  air  is  withdrawn  from  the  vessel,  and,  conse- 
quently, the  skin  within  the  mouth  of  the  vessel  is  relieved 
from  its  pressure.  All  the  other  parts  of  the  body,  however, 
being  still  subject  to  the  atmospheric  pressure,  and  the  elastic 
force  of  the  fluids  contained  in  the  body  having  an  equal  de- 
gree of  tension,  that  part  of  the  skin  which  is  thus  relieved 
from  the  pressure  will  be  swelled  out,  and  will  have  the  ap- 
pearance of  being  sucked  into  the  cupping  glass.  If  the  skin 
be  punctured  by  lancets,  the  blood  will  thus  be  drawn  from  it 
in  a  peculiar  manner. 

(160.)  That  the  presence  of  air  is  necessary  for  the  trans- 
mission of  sound  may  be  strikingly  illustrated  by  the  air  pump. 
A  small  apparatus,^1.  30.,  which,  by  being  drawn  upwards  and 

Fig.  30. 


20 


234 


A    TREATISE    ON    PNEUMATICS. 


CHAP.    V. 


downwards  alternately,  causes  a  bell  to  ring,  is  placed  on  the 
pump  plate,  and  covered  by  a  receiver  with  an  open  top.  A 
brass  cover,  furnished  with  a  sliding  rod,  is  placed  upon  this. 
The  sliding  rod  is  terminated  in  a  hook,  which  catches  the  ap- 
paratus, and  by  which  it  may  be  alternately  raised  and  lowered, 
without  allowing  any  air  to  pass  into  the  receiver.  The  appa- 
ratus being  thus  suspended  in  the  receiver  by  a  silken  thread, 
so  that  it  shall  not  touch  the  bottom  or  sides,  let  the  air  be 
exhausted  by  the  pump.  When  the  rarefaction  has  been 
carried  to  a  sufficient  extent,  let  the  rod  be  alternately  raised 
and  lowered,  so  that  the  bell  shall  ring.  It  will  be  found  to  be 
inaudible. 

If  the  air  be  now  gradually  admitted,  the  sound  will  at  first 
be  barely  audible,  but  will  become  louder  by  degrees,  until  the 
receiver  is  again  filled  with  air,  in  the  same  state  as  the  exter- 
nal atmosphere.  In  this  experiment  care  must  be  taken  not  to 
let  the  sounding  apparatus  rest  on  the  pump  plate,  for  it  will 
then  communicate  a  vibration  to  that,  which  will  finally  affect 
the  external  air,  and  produce  a  sound. 

The  Condensing  Syringe. 

condensing  syringe  is  an  instrument  by  which  a 
greater  quantity  of  air  may  be  forced  into  a 
vessel  than  that  vessel  contains  when  it  has 
a  free  communication  with  the  external  at- 
mosphere. 

Let  A  B,  Jig.  31.,  be  a  cylinder  furnished 
with  a  piston  P,  which  moves  air-tight  in  it. 
Let  C  be  a  tube  proceeding  from  the  bottom, 
and  furnished  with  a  stopcock.  Let  us  sup- 
pose this  tube  to  communicate  with  the  re- 
ceiver or  vessel  R,  in  which  it  is  intended  to 
condense  the  air.  Let  another  tube  D  pro- 
ceed from  the  cylinder,  also  furnished  with  a 
stopcock.  Let  the  piston  be  now  drawn  to 
3  the  top  of  the  cylinder,  both  stopcocks  being 
open.  The  receiver  R  being  in  free  com- 
munication with  the  atmosphere,  will  contain 
air  of  the  same  density  and  pressure  as  the 
external  atmosphere.  Let  'the  stopcock  D 
be  now  closed,  and  let  the  piston  be  pressed 
to  the  bottom  of  the  cylinder ;  the  air  confined 
in  the  cylinder  below  the  piston  will  thus  be 
forced  through  the  tube  C  into  the  vessel  R, 
while  the  piston  is  pressed  against  the  bottom 
B.  Let  the  stopcock  C  be  closed,  so  as  to 


CHAP.    V. 


CONDENSING    SYRINGE. 


235 


prevent  the  escape  of  the  air  from  the  vessel  R,  and  let  the 
stopcock  D  be  opened,  so  as  to  allow  a  free  communication 
between  the  cylinder  A  B  and  the  external  atmosphere.  Let 
the  piston  be  again  drawn  to  the  top  of  the  cylinder.  The 
cylinder  will  then  be  filled  with  atmospheric  air  of  the  same 
density  as  the  external  atmosphere.  Let  the  stopcock  D  be 
closed  and  C  opened,  and  let  the  piston  be  once  more  forced  to 
the  bottom  of  the  cylinder;  the  contents  of  the  cylinder  will  be 
thus  again  discharged,  and  forced  into  the  receiver  R.  Let 
the  stopcock  C  be  again  closed,  and  let  the  process  be  repeated. 
It  is  evident  that  at  each  stroke  of  the  piston  a  volume  of  at- 
mospheric air  vrill  be  forced  into  the  receiver  equal  to  the 
dimensions  of  the  cylinder  A  B ;  and  there  is  no  limit  to  the 
degree  of  condensation,  except  that  which  depends  on  the 
strength  of  the  receiver  R,  and  the  cylinder  and  tubes,  and  on 
the  power  by  which  the  piston  is  urged. 

After  each  stroke  of  the  piston,  the  density  of  the  air  in  R  is 
increased  by  the  admission  of  as  much  atmospheric  air  as  fills 
the  cylinder  A  B,  and  therefore  the  density,  as  the  process  ad- 
vances, receives  equal  increments  at  each  stroke  of  the  piston. 
Let  us  suppose  that  the  receiver  R  has  ten  times  the  capacity 
of  the  cylinder  A  B,  and  let  us  suppose  that  the  elastic  pressure 
of  the  air  in  R  at  the  commencement  of  the 
Fig.  32.  .        operation  is  expressed  by  the  number  10. 
After  the  first  stroke  this  pressure  will  be 
expressed  by  the  number  II,  inasmuch  as 
the  quantity  of  air  in  R  has  been  increased 
by  one  tenth  part  of  its  volume.     After  the 
second  stroke  the  pressure  will  be  express- 
ed by  the  number  12  ;  after  the  third  by 
the  number  13,  and  so  on. 

In  the  form  given  in  practice  to  the  con- 
densing syringe,  the  necessity  for  manipu- 
lating by  the  stopcocks  here  represented  is 
removed.  A  silk  valve,  such  as  that  de- 
scribed in  the  exhausting  syringe  is  placed 
in  the  tube  C,  jig.  32.,  but  opening  down- 
wards. The  neck  of  the  receiver  R  is  fur- 
nished with  a  stopcock  and  a  tube,  which 
terminates  in  a  screw.  This  screw  is  con- 
nected with  a  corresponding  one  proceeding 
from  the  bottom  of  the  syringe.  By  this 
arrangement,  the  air  is  capable  of  passing 
through  the  silk  valve  from  the  syringe  to 
the  receiver,  but  not  in  a  contrary  direction. 
A  small  hole  is  made  through  the  piston, 
extending  from  the  upper  to  the  lower  sur- 


236  A    TREATISE    ON    PNEUMATICS.  CHAP.    V. 

face,  and  the  silk  valve  is  extended  across  this  hole  on  the 
lower  surface,  so  that  air  is  capable  of  passing  through  this 
valve  to  the  cylinder  below  it,  but  not  in  a  contrary  direction. 

Now  let  us  suppose  that  the  air  in  the  receiver  has  the  same 
pressure  and  density  as  the  external  atmosphere,  and  let  the 
piston  P  be  at  the  top  of  the  cylinder,  the  air  in  the  cylinder 
A  B  also  having  the  same  pressure  and  density  as  the  external 
air.  By  pressing  the  piston  towards  the  bottom  of  the  cylinder, 
the  air  enclosed  will  become  condensed,  and  by  its  increased 
pressure  will  open  the  valve  V,  and  as  the  piston  descends  will 
be  forced  into  the  receiver  R.  When  the  piston  has  arrived  at 
the  bottom,  all  the  air  contained  in  the  cylinder  will  be  trans- 
ferred into  the  receiver.  It  will  be  retained  there,  because  the 
valve  V,  opening  downwards,  will  not  permit  its  return.  If  the 
piston  be  now  drawn  up,  it  will  leave  a  vacuum  below  it  when 
it  begins  to  ascend,  but  the  pressure  of  the  atmosphere  above 
will  open  the  valve  V ,  and  the  air  rushing  through  will  fill  the 
cylinder  as  the  piston  ascends  ;  and  when  the  piston  has  arrived 
at  the  top  of  the  cylinder,  the  space  below  it  will  again  be 
filled  with  atmospheric  air.  By  the  next  descent  of  the  piston 
this  air  is  forced  into  the  receiver  R  as  before,  and  so  the  pro- 
cess is  continued. 

It  should  be  observed,  that  when  the  piston  P  is  drawn  to  the 
top  of  the  cylinder,  the  air  which  has  passed  into  A  B  has  not 
quite  so  great  a  pressure  as  the  external  atmosphere.  This 
arises  from  the  valve  V  requiring  some  definite  force,  however 
small,  to  open  it.  When  the  air  which  has  passed  into  the 
chamber  A  B  acquires  a  pressure  which  is  less  than  the  atmos- 
pheric pressure  by  an  amount  equr.l  to  the  tension  of  the  valve 
V',  then  the  excess  of  the  pressure  of  the  atmosphere  over  the 
resistance  of  the  air  contained  in  A  B  will  be  insufficient  to 
open  the  valve  V,  and  no  more  air  can  pass  into  the  cylinder. 
It  should  also  be  observed,  that  the  valve  V,  being  pressed  up- 
wards by  the  elastic  force  of  the  air  condensed  in  the  receiver, 
requires  a  still  greater  pressure  than  this  to  open  it,  and  there- 
fore before  the  valve  V  can  be  opened,  the  air  enclosed  below 
the  piston  P  must  always  be  condensed  by  the  pressure  of  the 
piston  in  a  higher  degree  than  the  air  is  condensed  in  the  re- 
ceiver. The  observations  which  have  been  made  respecting 
the  limit  of  the  operation  of  the  exhausting  syringe,  arising 
from  mechanical  imperfections  and  other  causes,  will  also  be 
applicable  here.  However  nicely  the  piston  P,  and  the  cylin- 
der in  which  it  plays,  may  be  constructed,  there  will  still  be 
some  small  space  remaining  between  it  and  the  silk  valve  V, 
when  it  is  pressed  to  the  bottom  of  the  cylinder.  Into  this 
space  the  air  contained  in  the  cylinder  may,  finally,  be  con- 
densed ;  and  when  the  pressure  of  the  air  contained  in  the 


CHAP.    V. 


THE    CONDENSER. 


237 


receiver  becomes  equal  to  the  pressure  of  the  air  condensed 
into  the  space  between  the  piston  at  the  bottom  of  the  cylinder 
and  the  silk  valve,  the  operation  of  the  instrument  must  neces- 
sarily cease  ;  for  then  the  utmost  degree  of  condensation  which 
can  be  produced  above  the  silk  valve  V  will  be  insufficient  to 
open  the  valve,  and  therefore  the  syringe  cannot  introduce 
more  air  into  the  receiver. 

The  Condenser. 

(163.)  The  condenser  has  the  same  relation  to  the  apparatus 
just  described,  as  the  air  pump  has  to  the  exhausting  syringe. 
The  condenser  consists  of  a  receiver  firmly  and  conveniently 
fixed,  communicating  by  a  tube  with  one  or  two  condensing 
syringes,  which  may  be  worked  in  the  same  manner  as  the  ex- 
hausting syringe  described  in  the  air  pump. 

In  the  use  of  such  an  instrument,  it  is  convenient  to  possess 
the  means  of  indicating  the  degree  of  condensation  which  has 
been  effected.  For  this  purpose  a  mercurial  gauge  is  used, 
analogous  to  that  which  is  applied  to  the  air  pump.  A  bent 


Fig.  33. 


tube,  ABC,  fig.  33.,  contains  a  small  quantity 
of  mercury,  S,  B,  S',  in  the  curved  part. 


When 

the  ends  of  the  tube  are  open,  and  in  free  com- 
munication with  the  atmosphere,  the  surfaces, 
S,  S',  will  stand  at  the  same  level.  The  ex- 
tremity C  is  furnished  with  a  stopcock,  by 
which  a  communication  with  the  atmosphere 
may  be  permitted  or  intercepted.  The  extrem- 
ity A  communicates  by  a  tube  with  the  receiver 
in  which  the  air  is  to  be  condensed.  At  the 
commencement  of  the  process,  before  any  con- 
densation has  taken  place,  the  stopcock  C  is 
closed,  and  the  air  included  between  it  and  the 
surface  S'  has  then  the  same  pressure  as  the 
external  atmosphere.  The'air  in  the  receiver 
having  also  that  pressure,  the  two  surfaces  S 
and  S'  necessarily  stand  at  the  same  level. 
When  the  condensation  of  air  in  the  receiver  commences,  the 
pressure  on  the  surface  S  is  increased  ;  therefore  that  surface 
falls,  and  the  surface  S'  rises.  The  pressure  of  the  air  con- 
densed in  the  receiver  will  thus  be  balanced  by  the  weight  of 
the  column  of  mercury  between  the  levels  S  and  S',  together 
with  the  pressure  of  the  air  enclosed  between  S'  and  C.  But 
by  what  has  been  proved  in  (133.)  it  follows,  that  the  pressure 
of  the  air  enclosed  in  S'  C  is  increased  in  the  same  proportion 
as  the  space  S'  C  has  been  diminished.  Now,  as  the  original 
pressure  of  the  c.::-  contained  in  this  space  was  equal  to  the 


238  A    TREATISE    ON    PNEUMATICS.  CHAP.    VI. 

pressure  of  the  atmosphere,  it  is  always  easy  to  find  the  pres- 
sure of  the  air  reduced  in  bulk  by  increasing  the  amount  of 
atmospheric  pressure  in  the  same  proportion  as  the  space  S'  C 
has  been  diminished.  Thus,  if  the  air  enclosed  in  the  tube  be 
reduced  to  half  its  original  bulk,  then  the  pressure  it  exerts 
will  be  double  the  atmospheric  pressure.  If  it  is  reduced  to 
two  thirds  of  its  bulk,  then  the  pressure  of  the  enclosed  air  will 
be  to  the  atmospheric  pressure  in  the  proportion  of  three  to 
two,  and  so  on.  The  pressure  thus  computed  being  added  to 
the  pressure  arising  from  the  column  of  mercury  between  the 
levels  of  the  surfaces  S  and  S',  will  give  the  whole  pressure  of 
the  air  condensed  in  the  receiver. 

Although  the  condenser  is  not  without  its  use  in  experiment- 
al physics,  yet  it  is  an  instrument  far  less  important  than  the 
air  pump  to  which  it  is  so  analogous.  The  cases  are  innumer- 
able in  which  it  is  necessary  to  inquire  what  effect  would  take 
place  in  the  absence  of  the  atmosphere ;  but  they  are  com- 
paratively few  in  which  it  is  necessary  to  investigate  what 
effects  would  be  produced  under  increased  atmospheric 
pressure. 

We  do  not,  therefore,  think  it  necessary,  in  a  treatise  of  this 
nature,  to  enter  into  further  details  concerning  the  condenser. 


CHAP.  VI. 

MACHINES  FOR  RAISING  WATER. 

THE  LIFTING  PUMP. — PUMP  WITHOUT  FKICTION. — THE  SUCTION  PUMP. 
— THE  FORCING  PUMP. — THE  SAME  WITH  AIR  VESSEL."- THE  SAME 
WITH  A  SOLID  PLUNGER. — DOUBLE  FORCING  PUMP. — THE  FIRE  EN- 
GINE.— SIPHONS. — THE  WURTEMBURG  SIPHON. 

(164.)  MACHINES  of  a  great  variety  of  forms,  and  constructed 
upon  various  principles,  derived  from  mechanics,  hydrostatics, 
and  pneumatics,  have  been  applied  to  the  purposes  of  raising 
water  above  its  natural  level.  These  machines  generally  are 
called  Pumps. 

The  most  simple  machine  of  this  description  is  that  which  is 
called 

The  Lifting  Pump. 

(165.)  Let  A  B  D  C,fig.  34.,  be  a  short  cylinder  submerged 
in  the  well  or  reservoir  from  which  the  water  is  to  be  raised. 
This  cylinder  communicates  by  a  valve  x,  with  a  tube  or  pipe 


CHAP.    VI. 


LIFTING    PUMP. 


239 


Fig,  34. 


C  E,  which  is  carried  upwards  to  whatever  height  it  is  required 
to  raise  the  water.  A  piston  moves  water-tight  in  the  cylinder 
A  D,  and  is  worked  by  a  rod  or  frame- 
work, as  represented  in  the  figure. 
This  piston  is  furnished  with  a  valve  v, 
which  opens  upwards. 

When  the  piston  descends,  the  pres- 
sure of  the  water  opens  the  valve  i>,  and 
the  cylinder  between  the  two  valves  is 
filled  with  water.  When  the  piston 
is  raised,  the  water  between  the  valves 
being  pressed  against  the  yalve  x  opens 
it,  and  is  driven  into  the  tube  C  E, 
from  which  its  return  is  intercepted  by 
the  valve  x.  The  water  follows  the 
piston  in  its  ascent  by  the  hydrostatical 
pressure  of  the  water  in  the  reservoir 
outside  the  cylinder ;  and  on  the  next 
descent  of  the  piston,  water  will  again 
pass  through  the  valve  t>,  which  will  be 
driven  through  the  valve  r,  on  its  next 
ascent. 

The  use  of  the  valve  x  is  evidently 
to  relieve  the  valve  v  during  the  de- 
scent of  the  piston  from  the  pressure 
of  the  column  of  water  in  the  tube  C  E.  If  the  valve  v  were 
subject  to  that  pressure,  it  would  fail  to  be  opened  during  the 
descent  of  the  piston  by  the  pressure  of  the  water  in  the  well, 
because  the  level  of  that  water  is  necessarily  below  the  level 
of  the  water  in  the  pipe  C  E. 

The  use  of  the  valve  v  is  to  prevent  the  return  of  the  water 
through  the  piston  during  its  ascent.  In  drawing  up  the  piston 
a  force  will  be  necessary  sufficient  to  support  the  entire  column 
of  water  from  the  valve  v  to  the  surface  of  the  water  in  the 
tube  C  E.  The  actual  amount  of  this  force  is  the  weight  of  a 
column  of  water,  whose  base  is  equal  to  the  horizontal  section 
of  the  piston,  and  whose  height  is  equal  to  the  height  of  the 
surface  of  the  water  in  the  tube  C  E  above  the  valve  v.  It  is 
evident  that  after  each  stroke  of  the  pump,  the  pressure  on  the 
piston,  and  the  force  necessary  to  raise  it,  will  be  increased  by 
the  weight  of  a  column  of  water  whose  base  is  the  horizontal 
section  of  the  piston,  and  whose  height  is  equal  to  the  increase 
which  the  elevation  of  the  column  in  C  E  receives  from'  the 
water  driven  through  the  valve  x. 

(166.)  The  ingenious  form  of  pump  represented  in  fig.  35. 
acts  upon  the  principle  of  the  lifting  pump,  though  very  differ- 
ent from  it  in  appearance.  It  is  recommended  by  the  circum- 


240 


TREATISE    ON    PNEUMATICS. 


CHAP.    VI. 


Fig.  35. 


stance  of  being  free  from  friction,  or  nearly  so,  and  by  being 
capable  of  being  worked  by  the  weight  of  an  animal  walking  up 
an  inclined  plane,  one  of  th«  most  advantageous  ways  in  which 
animal  power  can  be  applied. 

Let  A  B  C  D  be  a  wooden  tube  of  any 
shape,  round  or  square,  which  descends  to  a 
depth  in  the  well  or  reservoir  equal  to  the 
height  above  the  surface  of  the  reservoir  to 
which  the  water  is  required  to  be  raised. 
Thus  if  A  H  be  the  height  to  which  the  water 
is  to  be  raised  above  the  level  of  the  well, 
then  the  depth  G  B  must  be  at  least  equal  to 
AH.  L  M  is  a  heavy  beam  or  plunger,  sus- 
pended from  a  chain,  and  capable  of  descend- 
ing by  its  own  weight  in  water.  A  valve  v 
covers  an  opening  placed  at  the  bottom  of  the 
tube  or  barrel.  By  the  hydrostatic  pressure 
the  water  will  enter  the  valve  v,  and  fill  the 
barrel  to  the  level  of  the  water  in  the  cistern. 
G  I  is  a  short  tube  proceeding  from  the  side 
of  the  barrel,  at  the  surface  of  the  water,  and 
communicating  with  the  vertical  tube  A  H 
by  a  valve  H,  which  opens  upwards.  K  is 
the  spout  of  discharge.  The  plunger  L  M 
hangs  loosely  in  the  tube,  so  that  it  moves 
upwards  and  downwards  perfectly  free  from 
friction.  When  this  plunger  is  allowed  to 
descend  by  its  weight  into  the  water  which 
fills  the  lower  part  of  the  tube,  the  valve  v  is 
closed,  and  the  water  displaced  by  the  plunger 
is  forced  through  the  valve  H  into  the  tube 
A  H.  When  the  plunger  is  raised,  the  valve 
H  is  closed,  and  the  water  thus  forced  into  the  tube  A  H 
cannot  return.  The  water  from  the  cistern  then  flows  through 
the  valve  v,  and  rises  in  the  tube  to  the  level  G.  The  next 
descent  of  the  piston  propels  more  water  into  the  tube  A  H, 
and  this  is  continued  so  long  as  the  piston  is  worked. 

The  manner  in  which  such  an  apparatus  is  worked  by  the 
weight  of  a  man  is  represented  in  Jig.  36.  Two  pumps  are 
used,  such  as  that  just  described,  and  when  the  plunger  de- 
scends in  one  it  rises  in  the  other.  The  two  pumps  communi- 
cate with  one  vertical  pipe,  which  therefore  receives  a  continual 
supply  of  water ;  for  while  the  action  of  one  pump  is  suspend- 
ed, the  other  is  in  progress.  A  man  walks  from  one  end  of  an 
inclined  plane  to  the  other,  and,  by  his  weight  upon  one  side 
or  the  other  of  the  fulcrum,  causes  the  plungers  alternately  to 
rise  and  fall. 


CHAP.    VI, 


241 


The  Suction  Pump. 

(167.)  The  common  suction  pump  is  a  large  syringe,  which 
is  connected  with  a  tube,  the  lower  extremity  of  which  is  plunged 
in  a  well,  from  which  water  is  to  be  raised.  This  tube  is 
called  a  suction  pipe. 

Let  W,^§T.  37.,  represent  the  well  or  reservoir  from  which 
the  water  is  to  be  elevated,  and  let  S  O  represent  the  suction 
tube.     The  lower  end  O  of  this  tube  being  pierced  with  holes 
acts  as  a  strainer,  and  prevents  the  admission  of  solid  impurities 
into  the  pipe  which  might  choke  the  pump  and  impede  its 
action.     At  the  upper  end  of  the  suction  tube  a  valve  x  is  placed 
which  opens  upwards,  and  at  this  point  the  tube  is  connected 
with  the  great  syringe  B  C,  furnished  with  a  piston,  in  which 
there  is  another  valve  v,  which  also  opens  upwards,  as  already 
described  in  the  exhausting  syringe.     The  piston  is  worked 
alternately  upwards  and  downwards  in  common  pumps  by  a 
lever,  called  the  brake,  but  may  also  be  worked  in  many  other 
ways.     At  the  commencement  of  the  operation,  the  level  of  the 
water  in  the  suction  tube  coincides  with  the  level  of  the  exter- 
nal water  in  the  well,  because  both  are  subject  to  the  same 
atmospheric  pressure  ;  but  when  the  syringe  B  C  is  worked,  it 
will  rarefy  the  air  in  the  tube  S  O.  on  the  principle  and  in  the 
manner  explained  in  (148.).     The  pressure  of  the  air  in  S  O  on 
the  surface  of  the  water  within  it  being  thus  diminished,  and 


242 


A    TREATISE    ON    PNEUMATICS.  CHAP.  Yl. 


Fig.  37. 


rendered  less  than  the  pressure  of  the  atmosphere  on  the  exte- 
rior surface  of  the  water  in  the  well,  a  column  of  water  will  be 
forced  in  the  tube  S  O  by  the  excess  of  the  atmospheric  pres- 
sure. In  proportion  as  the  rarefaction  of  the  air  between  the 
surface  of  the  column  suspended  in  the  tube  S  O  and  the  valve 
x  is  increased,  in  the  same  proportion  will  its  pressure  on  the 
surface  of  the  column  be  diminished,  and  so  long  as  this  dimi- 
nution is  continued  the  height  of  the  column  will  increase. 
There  is,  however,  a  limit  to  this  height.  If  the  air  could  be 
altogether  withdrawn  from  the  tube  S  O,  and  an  absolute 
vacuum  produced  beneath  the  valve  x,  like  that  which  exists 
above  the  mercury  in  the  barometer,  then  the  atmospheric  pres- 
sure, acting  with  undiminished  effect  on  the  surface  of  the 
water  in  the  well,  would  sustain  a  column  of  water  in  the  tube 
S  O,  the  weight  of  which  would  be  equal  to  a  column  of  mer- 
cury with  the  same  base,  and  having  the  height  of  the  mercury 
in  the  barometer.  Now  the  specific  gravity  of  water  is  about 
13i  times  less  than  that  of  mercury,  and  consequently  a  force 
which  could  sustain  a  column  of  30  inches  of  mercury  would 


CHAP.  VI.  SUCTION  PUMP.  243 

support  a  column  of  water  13^  times  greater  in  height.  If  the 
barometer,  therefore,  be  considered  to  stand  at  30  inches,  the 
atmospheric  pressure  would  support  a  column  of  water  of  about 
405  inches,  or  34  feet.  From  this  consideration  it  will  appear 
that  if  the  operation  of  the  syringe  were  perfect,  and  that  an 
absolute  vacuum  could  be  produced  below  the  valve  #,  still  the 
water  could  never  ascend  through  that  valve  by  the  atmospheric 
pressure,  if  its  height  above  the  level  of  the  water  in  the  cistern 
exceeded  13^  times  the  height  of  the  barometric  column.  In 
these  countries  the  barometric  column  varies  between  28  and 
31  inches  in  height,  and  therefore  the  valve  x  ought  not  to  be 
more  than  30  feet  above  the  level  of  the  water  in  the  well. 
But  it  is  still  to  be  observed,  that  the  construction  and  opera- 
tion of  the  great  syringe  B  C  is  subject  to  inevitable  imperfec- 
tions, which  are  always  greater  the  larger  the  scale  on  which 
the  instrument  is  made.  Even  in  small  syringes  accurately 
constructed,  a  degree  of  imperfection  exists,  which  has  been 
already  noticed  in  the  explanation  of  the  exhausting  syringe  ; 
but  such  defects  are  greatly  increased  in  a  larger  syringe,  such 
as  that  used  in  common  water  pumps,  where  a  common  and  less 
expensive  mode  of  construction  must  be  used. 

From  these  causes,  a  column  of  water,  which  can  be  raised 
in  the  tube  S  O,  will  be  less  than  even  30  feet  in  height.  It  is 
obvious,  however,  that  within  this  limit  the  length  of  the  tube 
S  O  must  be  determined  by  the  degree  of  excellence  attained 
in  the  construction  of  the  syringe  C  B. 

When  the  rarefaction  has  been  carried  to  a  sufficient  extent, 
the  tube  S  O  being  adjusted  to  a  proper  length,  the  column  of 
trater  will  rise  until  part  of  it  pass  through  the  valve  x,  and  it 
will  ascend  to  a  level  in  the  syringe  B  C,  the  height  of  which 
above  the  water  in  the  well  will  be  determined  by  the  excess 
of  the  atmospheric  pressure  above  the  pressure  which  continues 
to  act  on  the  surface  of  the  water  in  C  B.  The  water  which  is 
thus  drawn  into  the  syringe  presses  by  its  weight  on  the  valve 
x,  and  cannot  return  into  the  suction  tube.  When  the  piston  is 
now  pressed  down,  it  will  act  on  tKe  water  which  has  been 
raised  above  the  valve  x  in  the  manner  of  the  lifting  pump 
already  described,  and  the  remainder  of  the  process  in  raising 
the  water  will  be  in  all  respects  the  same  as  that  which  has 
been  explained  in  reference  to  the  lifting  pump.  In  this  case 
the  water  raised  through  the  suction  pipe,  and  deposited  above 
the  valve  x  in  the  syringe,  serves  as  a  well  to  the  syringe,  con- 
sidered as  a  lifting  pump.  It  is  evident  that,  according  as  the 
water  is  elevated  above  the  piston,  the  ^atmospheric  pressure 
acting  on  the  surface  of  the  water  in  the  well  will  force  more 
water  through  the  valve  x.  In  this  way  the  process  is  contin- 
ued ;  during  every  ascent  of  the  piston  water  being  raised 


244 


A    TREATISE    ON    PNEUMATICS. 


CHAP.    VI. 


through  the  valve  a:,  and  during  each  descent  of  the  piston  the 
same  quantity  of  water  passing  through  the  valve  v.  As  the 
water  accumulates  above  the  piston,  as  described  in  the  lifting 
pump,  it  at  length  reaches  the  spout  from  which  it  is  dis- 
charged. 

Fig.  37. 


Such  is  the  construction  and  operation  of  the  common  house- 
hold pump.  It  may  appear,  at  first  view,  that  the  pressure  of 
the  atmosphere  sustaining  the  column  of  water  in  the  suction 
tube  furnishes  an  aid  to  the  power  which  works  the  pump. 
This,  however,  is  not  the  case  ;  at  least  not  so  in  the  sense  in 
which  it  is  commonly  understood.  To  make  this  intelligible,  it 
will  be  necessary  to  consider  somewhat  in  detail  the  forces 
which  are  in  operation  during  the  process.  There  are  some 
forces  which  are  directed  downwards  from  the  top  of  the  syringe 
towards  the  bottom  of  the  well,  and  others  which  are  directed 
upwards.  Now  it  is  evident  that  the  mechanical  power  applied 
to  draw  the  piston  up  will  have  to  overcome  all  that  excess  by 
which  the  forces  downwards  exceed  the  forces  upwards.  Let 


CHAP.    VI.  SUCTION    PUMP.  245 

us  suppose  a  column  of  water  resting  on  the  piston,  after  having 
passed  through  the  valve  v.  The  upper  surface  of  this  column 
is  pressed  upon  by  the  weight  of  the  atmosphere  ;  the  piston 
has,  therefore,  this  weight  to  sustain.  It  has  also  to  sustain 
the  weight  of  the  water  which  is  above  it.  The  atmospheric 
pressure  acting  also  on  the  water  in  the  well,  is  transmitted  by 
the  quality  of  liquids  explained  in  Hydrostatics,  chap,  ii.,  to 
the  bottom  of  the  piston  ;  but  this  effect  is  diminished  by  the 
weight  of  the  column  of  water  between  the  surface  of  the  water 
in  the  well  and  the  bottom  of  the  piston,  for  the  atmospheric 
pressure  must,  in  the  first  place,  sustain  that  column,  and  can 
only  act  upon  the  bottom  of  the  piston  in  the  upward  direction 
with  that  amount  of  force  by  which  it  exceeds  the  weight  of  the 
column  of  water  between  the  piston  and  the  well.  The  effect, 
therefore,  on  the  piston  is  the  same  as  if  it  were  pressed  down- 
wards by  the  Aveight  of  the  column  of  water  between  the  piston 
and  the  well,  and  at  the  same  time  pressed  upwards  by  the 
atmospheric  pressure.  Thus  the  piston  may,  in  fact,  be  regard- 
ed as  being  urged  downwards  by  the  following  forces, — the 
atmospheric  pressure,  the  weight  of  the  water  above  the  piston, 
and  the  weight  of  the  water  between  the  piston  and  the  well ; 
that  is  to  say,  in  fact,  by  the  atmospheric  pressure,  together 
with  the  weight  of  all  the  water  which  has  been  raised  from  the 
well.  At  the  same  time,  it  is  pressed  upwards  by  the  atmos- 
pheric pressure  transmitted  from  the  surface  of  the  water  in  the 
well.  .This  upward  pressure  will  neutralize  or  destroy  the 
effect  of  the  same  atmospheric  pressure  acting  downwards  on 
the  surface  of  the  water  above  the  piston,  and  the  effective 
downward  force  will  be  the  weight  of  all  the  water  which  is 
contained  in  the  pump. 

By  this  reasoning,  it  appears  that  the  pump  must  be  worked 
with  as  much  force  as  is  equal  to  the  weight  of  all  the  water 
which  is  in  it  at  any  time,  and,  therefore,  that  the  atmospheric 
pressure  affords  no  aid  to  the  working  power. 

Since  the  action  of  the  pump  in  raising  water  is  subject  to 
intermission,  the  stream  discharged  from  the  spout  will  neces- 
sarily flow  by  fits  and  irregularly,  if  some  means  be  not  adopted 
to  prevent  this.  At  the  top  of  the  pump  a  cistern  may  be  con- 
structed, with  a  view  to  remove  this  inconvenience.  If  the 
pump  be  worked,  in  the  first  instance,  so  as  to  raise  more  water 
in  a  given  time  than  is  discharged  at  the  spout,  the  column  of 
water  will  necessarily  accumulate  in  the  barrel  of  the  pump 
above  the  spout.  The  cistern  M  N  will,  therefore,  be  filled, 
and  this  will  continue  until  the  elevation  of  the  surface  of  the 
water  in  the  cistern  above  the  spout  will  produce  such  a  pres- 
sure, that  the  velocity  of  discharge  from  the  spout  will  be  equal 
to  the  velocity  with  which  the  water  is  raised  bv  the  piston. 
21* 


246 


A    TREATISE    ON    PNEUMATICS. 


CHAP.    VI. 


The  level  of  the  water  in  the  cistern  will  therefore  cease  to 
rise.  This  level,  however,  will  be  subject  to  a  small  variation 
as  the  piston  rises  ;  for  while  the  piston  is  descending,  the 
water  is  flowing  from  the  spout,  and  no  water  is  raised  by  the 
piston ;  consequently  the  level  of  the  water  in  the  cistern  falls. 
When  the  piston  rises,  water  is  raised,  and  the  quantity  in  the 
cistern  is  increased  faster  than  it  flows  from  the  spout ;  conse- 
quently the  level  of  the  water  in  the  cistern  rises,  and  thus  this 
level  alternately  rises  and  falls  with  the  piston.  But  if  the 
magnitude  of  the  cistern  be  much  greater  than  the  section  of 
the  pump  barrel,  then  this  variation  in  the  surface  will  be  pro- 
portionally small,  for  the  quantity  of  water  which  fills  a  part  of 
the  barrel,  equal  to  the  play  of  the  piston,  will  produce  a  very 
slight  change  in  the  surface  of  the  water  in  the  cistern.  The 
flow,  therefore,  from  the  spout  S  will  be  uniform,  or  nearly  so. 

The  Forcing  Pump. 

(168.)  The  forcing  pump  is  an  instrument  which  combines 
the  principles  of  the  suction  and  the  lifting  pump.     In  Jig.  38., 

Fig.  38. 


C  E  is  a  suction  pipe  which  descends  into  the  well,  at  the  top 
of  which  is  the  suction  valve  V  opening  upwards.  The  pump 
barrel  A  B  C  D  is  furnished  with  a  solid  piston  without  a  valve, 
and  from  the  side  of  this  barrel,  just  above  the  suction  valve, 
there  proceeds  a  pipe  which  communicates  with  an  upright 
cylinder  G  H,  which  is  carried  to  the  height  to  which  the  water 
is  intended  to  be  raised.  In  the  bottom  cf  this  cylinder  is 


CHAP.  VI.  FORCING    1'UMP.  247 

placed  a  valve  V,  which  opens  upwards.  In  the  commence- 
ment of  the  process,  the  suction  pipe  C  E,  and  the  chamber 
between  the  piston  and  valves,  are  filled  with  air.  When  the 
piston  is  depressed  to  the  valve  V,  the  air  enclosed  in  the  latter 
chamber  becomes  condensed,  and,  opening  the  valve  V',  a  part 
of  it  escapes.  On  raising  the  piston  the  air  below  it  becomes 
rarafied,  and  the  air  in  the  suction  pipe,  opening  the  valve  V  by 
its  superior  pressure,  expands  into  the  upper  chamber :  a  part 
of  it  is  expelled  through  the  valve  V7,  when  the  piston  next 
descends.  During  this  process,  it  is  evident  that  the  pump  acts 
as  an  air  pump  or  exhausting  syringe,  and  is  in  all  respects 
equivalent  to  the  instrument  described  in  (148.).  When  the  air 
becomes  sufficiently  rarefied  by  this  process,  the  atmospheric 
pressure  forces  water  from  the  well  through  the  suction  pipe 
and  the  valve  V  into  the  chamber  between  the  piston  and  the 
valves.  When  the  piston  now  descends,  it  presses  on  the  sur- 
face of  the  water,  and  the  valve  V  opening  upwards  prevents 
the  return  of  the  water  into  the  suction  pipe  ;  while  the  pres- 
sure of  the  piston,  being  transmitted  by  the  water  to  the  valve 
V,  opens  it,  and,  as  the  piston  descends,  the  water  passes  into 
the  force  pipe  G  H.  The  next  ascent  of  the  piston  allows  more 
water  to  pass  through  the  valve  V,  and  the  next  descent  forces 
this  water  through  the  valve  V  into  the  force  pipe.  By  contin- 
uing this  process,  the  quantity  of  water  in  the  force  pipe  con- 
tinually increases,  receiving  equal  additions  at  each  descent  of 
the  piston. 

It  is  evident  that  the  force  pipe  may  be  placed  in  any  posi- 
tion, whether  perpendicularly,  obliquely,  or  horizontally,  and 
that,  in  every  case,  the  action  of  the  piston  will  propel  the  water 
through  it. 

When  the  piston  is  pressed  downwards,  and  the  valve  V'  is 
opened,  it  is  necessary  that  the  force  which  works  the  piston 
should  balance  the  weight  of  the  column  of  water  in  the  force 
pipe,  for  this  weight  is  transmitted  by  the  water  between  the 
piston  and  force  pipe  to  the  bottom  of  the  piston ;  consequently, 
the  height  of  the  column  of  water  in  the  force  pipe  will  measure 
the  intensity  of  the  pressure  against  the  base  of  the  piston  when 
the  valve  V  is  open.  A  column  of  water  about  34  feet  in 
height,  suspended  in  the  force  pipe,  will  press  on  the  base  of 
the  piston  with  a  force  of  about  15  pounds  on  each  square  inch, 
and  the  pressure  at  other  heights  will  be  proportional  to  this. 
The  force  necessary  to  urge  the  piston  downwards  may,  there- 
fore, always  be  calculated.  In  drawing  the  piston  up,  the  valve 
V'  is  closed,  and  relieves  the  piston  from  the  weight  of  the 
incumbent  column ;  if  the  valve  V  is  opened,  the  piston  is  sub- 
ject to  the  same  pressure  as  in  the  suction  pump.  This  pres- 
sure has  been  already  proved  to  be  equal  to  the  weight  of  the 


248 


A    TREATISE    ON    PNEUMATICS. 


CHAP.  VI. 


column  of  water  raised  above  the  level  of  the  water  in  the 
well. 

It  follows  from  this,  that  if  the  height  of  the  force  pipe  be 
equal  to  the  length  of  the  suction  pipe,  then  the  piston  must  be 
pressed  upwards  and  downwards  with  the  same  force ;  but  if 
the  height  of  the  force  pipe  be  greater  or  less  than  the  length 
of  the  suction  pipe,  then  the  downward  pressure  must  be  greater 
or  less,  in  the  same  proportion,  than  the  force  which  draws  the 
piston  up.  In  fact,  the  force  which  draws  the  piston  up  in  this 
pump,  after  the  water  has  been  raised  to  the  valve,  is  uniform  ; 
while  the  force  with  which  the  piston  must  be  urged  down- 
wards is  continually  increasing,  until  the  water  in  the  force  pipe 
reaches  its  point  of  discharge,  and  until  the  discharge  becomes 
equal  to  the  supply. 

The  supply  of  water  by  the  force  pipe  through  the  valve  V', 
is  evidently  intermitting,  being  suspended  during  the  ascent  of 
the  piston  ;  it  follows,  therefore,  that  the  flow  from  the  point  of 
discharge  will  be  liable  to  the  same  intermission,  if  means  be 
not  adapted  to  counteract  this  effect.  A  cistern  placed  at  the 
top  of  the  force  pipe,  as  already  described  in  the  suction  pump, 
may  serve  the  purpose,  but  it  is  generally  more  convenient  to 
use  an  apparatus  called  an  air  vessel,  which  is  represented  in 
Jig.  39.  Immediately  above  the  valve  V  a  short  tube  commu- 


nicates  with  a  strong,  close  vessel  of  sufficient  capacity  ;  through 
the  top  of  this  vessel  the  force  pipe  G  H  passes,  and  descends 
to  a  point  near  the  bottom.  By  the  action  of  the  pump  the 
water  is  forced  into  the  vessel  M  N,  and  when  its  surface  rises 
above  the  mouth  H  of  the  force  pipe,  the  air  in  the  vessel  M  N 
is  confined  above  the  water ;  and  as  the  water  is  gradually 
forced  in,  this  air  is  compressed,  and  acts  with  increased  elastic 


CHAP.  VI.  AIR    VESSEL.-  249 

force  on  the  surface  of  the  water :  this  pressure  forces  a  column 
of  water  into  the  pipe  H  G,  and  maintains  that  column  at  an 
elevation  proportional  to  the  elastic  force  of  the  condensed  air. 
When  the  air  in  the  vessel  M  is  reduced  to  half  its  original 
bulk,  it  will  act.  on  the  surface  of  the  water  with  double  the 
atmospheric  pressure  ;  meanwhile,  the  water  in  the  force  pipe 
being  subject  only  to  once  the  atmospheric  pressure,  there  is 
an  unresisted  upward  force  equal  to  the  atmospheric  pressure 
which  sustains  the  column  of  water  in  the  tube  :  a  column  will 
then  be  sustained  about  34  feet  in  height.  When  the  air  is 
reduced  to  one  third  of  its  original  bulk,  the  height  of  the  col- 
umn which  it  can  sustain  is  68  feet,  and  so  on.  If  the  force 
pipe  terminate  in  a  ball  pierced  with  small  holes,  so  as  to  form 
a.  jet  d'eau,  the  elastic  pressure  of  the  air  on  the  surface  will 
cause  the  water  to  spout  from  the  holes. 

It  is  of  great  importance  in  the  forcing  pump  that  the  piston 
should  be  truly  water-tight  in  the  cylinder,  and  in  practice  this 
is  not  always  very  easily  accomplished.  The  arrangement 
represented  in  Jig.  40.  is  better  adapted  to  insure  the  perfect 

Fig.  40. 


action  of  the  pump  than  the  form  of  piston  already  represented. 
In  this  case  a  polished  cylindrical  metal  plunger  P  passes 
through  a  collar  of  leathers  A  B,  which  exactly  fits  it ;  and  it  is 
maintained  perfectly  air-tight  and  water-tight  by  being  lubri- 
cated with  oil  or  tallow.  When  the  plunger  is  raised,  the  space 
it  deserts  is  replaced  by  the  water  which  rises  through  tho 


250  A    TREATISE    ON    PNEUMATICS.  CHAP.    VI. 

valve  V  ;  and  when  it  descends,  the  water  which  filled  the  space 
into  which  it  advances  is  driven  before  it,  through  the  valve  V, 
into  the  force  pipe. 

If  the  forcing  pump,  represented  in  Jig.  38.,  be  attentively 
considered,  it  will  be  perceived  that  the  principles  on  which 
the  piston  acts  in  its  ascent  and  descent  are  perfectly  distinct. 
In  its  ascent  it  is  employed  in  drawing  the  water  from  the  suc- 
tion pipe  into  the  pump  barrel,  and  in  its  descent  it  is  employed 
in  forcing  that  water  from  the  pump  barrel  into  the  force  pipe. 
Now  the  piston  being  solid,  and  not  furnished  with  any  valve, 
there  is  no  reason  why  its  upper  surface  should  not  be  employ- 
ed in  raising  or  propelling  water,  as  well  as  the  lower.  While 
the  lower  surface  is  employed  in  drawing  water  from  the  suc- 
tion pipe,  the  upper  surface  might  be  employed  in  propelling 
water  into  the  force  pipe  ;  and,  on  the  other  hand,  in  the  de- 
scent of  the  piston,  when  the  lower  surface  is  employed  in  pro- 
pelling water  into  the  force  pipe,  the  upper  surface  might  be 
engaged  in  drawing  water  from  the  suction  pipe.  To  accom- 
plish this,  it  is  only  necessary  that  the  top  of  the  cylinder  should 
be  closed,  and  that  the  piston  rod  should  play  through  an  air- 
tight collar,  the  top  of  the  cylinder  communicating  with 
force  pipe  and  the  suction  pipe,  as  well  as  the 

Such  an  arrangement  is  represented  in  Jig. 

Fig.  41. 


piston  ascends,  the  suction  valve  F  is  opened,  and  water  is 
drawn  into  the  pump  barrel  below  the  piston ;  and  when  the 


CHAP.    VI.  FIRE    ENGINE.  251 

piston  descends,  the  suction  valve  F  is  closed,  and  the  pressure 
of  the  piston  on  the  water  below  it  opens  the  valve  C,  and  pro- 
pels the  water  into  the  force  pipe  C  G.  Also,  while  the  piston 
is  descending,  water  rises  through  the  suction  valve  E  into  the 
barrel  above  the  piston ;  and  when  the  piston  ascends,  the 
water  being  pressed  upwards  keeps  the  valve  E  closed,  and 
opens  the  valve  D,  and  is  thus  propelled  into  the  force  pipe. 
By  this  arrangement  the  force  pipe  receives  a  continual  supply 
of  water  from  the  pump  barrel  without  any  intermission  ;  and 
in  like  manner  the  pump  barrel  receives  an  unremitting  flow 
from  the  suction  pipe.  This  will  be  distinctly  seen,  if  it  is  con- 
sidered that  either  of  the  two  suction  valves  E  or  F  must  be 
always  open.  If  the  piston  descends,  the  valve  E  is  open  and 
F  is  closed ;  and  if  the  piston  ascends,  the  valve  E  is  closed  and 
the  valve  F  is  open:  a  stream,  therefore,  continually  flows 
through  the  one  valve  or  the  other  into  the  pump  barrel.  In 
like  manner,  whether  the  piston  ascends  or  descends,  one  of 
the  valves  C  or  D  must  be  open  ;  if  it  descends,  the  valve  D 
is  closed  and  C  is  open ;  if  it  ascends,  the  valve  D  is  open  and 
C  is  closed. 

The  Fire  Engine. 

(109.)  The  fire  engine  is  subject  to  a  variety  of  different 
forms,  which  all,  however,  agree  in  one  principle.  It  generally 
consists  of  a  double  forcing  pump  communicating  with  the 
same  air  vessel,  and  instead  of  a  force  pipe  a  flexible  leather 
hose  is  used,  through  which  the  water  is  driven  by  the  pressure 
of  the  condensed  air  in  the  air  vessel.  A  section  of  the  ap 
paratus  is  represented  in  fig.  42.  T  is  a  pipe  which  descends 
into  the  receiver,  or  to  any  vessel  containing  the  supply  of 
water.  This  pipe  communicates  with  two  suction  valves  V, 
which  open  into  the  pump  barrels  of  two  forcing  pumps  A  B, 
in  which  solid  pistons  P  are  placed.  The  piston  rods  of  these 
are  connected  with  a  working  beam,  so  arranged  that  a  number 
of  different  persons  may  act  on  both  sides  of  it.  Force  pipes 
proceed  from  the  sides  of  the  pump  barrel  above  the  valves  V, 
and  they  communicate  with  an  air  vessel  M,  by  means  of  valves 
V',  which  also  open  upwards.  The  pipe  descends  into  the  air 
vessel  near  the  bottom,  as  already  described  in  jig.  39.  This 
pipe  is  connected  with  the  flexible  leathern  hose  L,  the  length 
of  which  is  adapted  to  the  purposes  to  which  the  machine  is  to 
be  applied.  The  extremity  of  the  hose  may  be  carried  in  any 
direction,  and  may  be  introduced  through  the  doors  or  windows 
of  buildings.  By  the  alternate  action  of  the  pistons,  water  is 
drawn  through  the  suction  valve,  and  propelled  through  the 
forcing  valves  V,  until  the  air  in  the  top  of  the  vessel  M  be- 


25* 


A    TREATISE    ON   PNEUMATICS.  CHAP.    VI. 


Fig.  42. 


comes  highly  compressed.  This  pressure  acts  continually  on 
the  surface  of  the  water  in  the  vessel,  and  forces  it  through  the 
leathern  hose,  so  as  to  spout  from  its  extremity  with  a  force 
depending  partly  on  the  degree  of  condensation,  and  partly  on 
the  elevation  of  the  extremity  of  the  hose  above  the  level  of 
the  engine.  It  is  to  be  considered  that  the  pressure  of  the 
condensed  air  has,  in  the  first  instance,  to  support  a  column  of 
water,  the  height  of  which  is  equal  to  the  level  of  the  end  of 
the  tube  above  the  level  of  the  water  in  the  air  vessel ;  and 
until  the  pressure  of  the  condensed  air  exceeds  what  is  neces- 
sary for  this  purpose,  no  water  can  spout  from  the  end  of  the 
hose  ;  and,  subsequently,  the  force  with  which  it  will  so  spout 
will  be  proportional  to  the  excess  of  the  pressure  of  the  con- 
densed air  above  the  weight  of  the  column  of  water,  whose 
height  is  equal  to  the  elevation  of  the  end  of  the  hose  above 
the  level  of  the  water  in  the  air  vessel.* 

The,  Siphon. 

(170.)  The  siphon  is  a  contrivance  by  which  a  liquid  may  be 
conducted  from  one  vessel  to  another  through  an  intermediate 
channel  or  pipe,  which  rises  above  the  natural  level  of  the 
liquid. 

Let  D,fg.  43.,  be  a  cistern  containing  a  liquid,  and  let  B  be 
the  height  over  which  it  is  necessary  to  conduct  that  liquid. 

*  The  resistance  of  atmospheric  pressure  is  not  here  considered. — AM.  ED 


CHAP.    VI. 


SIPHONS. 


253 


Let  A  B  C  be  a  bent  tube  open  at  both  ends,  and  let  the  leg 
B  A  be  immersed  in  the  liquid  which  it  is  required  to  transfer, 
and  let  the  end  C  be  directed  into  the  vessel  to  which  it  is  in- 

Fig.  4-3. 


tended  to  remove  it.  Let  the  air  which  fills  the  tube  D  B  C  be 
drawn  from  it  by  the  mouth  applied  at  C,  or  by  an  exhausting 
syringe.  The  atmospheric  pressure  immediately  taking  effect 
on  the  surface  D  of  the  water'  in  the  cistern  will  press  the 
water  into  the  tube  A  B,  towards  the  point  B  ;  and  if  the  point 
B  be  not  at  a  greater  height  above  the  level  of  the  cistern  than 
34  feet,  then  the  water  will  rise  to  the  highest  point  B,  and  will 
flow  so  as  to  fill  the  entire  tube  to  the  mouth  C. 

To  comprehend  the  principle  upon  which  the  siphon  acts,  let 
us  suppose  the  water  at  the  point  B  acted  upon  by  two  pres- 
sures, one  towards  C,  and  the  other  towards  D.  It  will  move 
in  the  one  direction  or  in  the  other  according  as  the  one  or  the 
other  pressure  prevails.  The  atmospheric  pressure  acting  on 
the  surface  D  supports  the  column  in  the  siphon  between  the 
surface  and  the  point  B,  and  it  presses  the  water  at  B  towards 
C  with  a  pressure  equal  to  the  amount  by  which  the  atmos- 
pheric pressure  exceeds  the  weight  of  the  column  D  B,  which 
it  sustains  in  the  siphon.  The  atmospheric  pressure  also  acts 
at  the  mouth  C  of  the  siphon,  and  is  resisted  by  the  weight  of 
.  the  column  C  B.  It  exerts  a  pressure  on  the  water  at  B, 
amounting  to  the  excess  of  the  atmospheric  pressure  above  the 
weight  of  the  column  C  B.  Thus  it  appears  that  the  water  at 
B  is  urged  towards  C  by  a  force  equal  to  that  pressure  by 
which  the  atmospheric  pressure  exceeds  the  weight  of  the 
water  in  B  D,  and  this  force  is  resisted  by  a  force  equal  to  that 
by  which  the  same  atmospheric  pressure  exceeds  the  weight 
of  the  water  in  C  B.  Now,  since  the  atmospheric  pressure 
exceeds  the  weight  of  the  water  in  D  B  by  a  greater  quantity 
22 


254 


A    TREATISE    ON    PNEUMATICS. 


CHAP.    VI. 


it  exceeds  the  weight  of  the  water  in  B  C,  it  follows  that 
B  will  be  urged  towards  C  with  a  greater  force  than  it  is  urged 
towards  D,  and,  therefore,  that  it  will  move  towards  C.  It  is 

Fig.  43. 


evident  that  the  excess  of  the  force  which  urges  it  towards  C 
above  the  force  which  urges  it  towards  D  will  be  equal  to  the 
weight  of  the  column  of  water  C  which  is  contained  in  the 
longer  leg  of  the  siphon  below  the  level  of  the  water  in  the 
cistern  D. 

If  the  leg  of  the  siphon  terminate  at  D',  the  forces  which 
would  act  on  the  water  at  B  would  be  equal,  for  the  one  would 
>e  the  atmospheric  pressure  diminished  by  the  weight  of  the 
water  in  B  D,  and  the  other  would  be  the  atmospheric  pressure 
diminished  by  the  weight  of  the  water  in  B  D' ;  but  the  weight 
of  the  water  in  BD  and  BD'  being  equal,  the  forces  which  act 
on  the  water  at  B  will  also  be  equal;  therefore  no  water  will 
flow  from  the  siphon.  If  the  leg  of  the  siphon  terminate  above 
D',  as  at  E,  then  the  pressure  on  the  water  at  B,  the  siphon 
being  supposed  to  be  filled,  will  be  greater  in  the  direction  at 
B  D  than  in  the  direction  at  B  C,  and,  therefore,  the  water  will 
flow  back  into  the  cistern,  and  the  siphon  will  be  useless 

Let  F  G  be  a  vessel  to  which  the  liquid  is  to  be  transferred 
When  it  rises  in  this  vessel  above  the  mouth  C  to  anv  higher 
leM^al^' thei!  *h\wei&ht  of  the  ^ater  in  the  leg  below  L 
will  be  balanced  by  the  pressure  of  the  water  in  the  vessel  F  G 
and,  therefore,  the  efficient  leg  of  the  siphon  will  be  B  L  Thus' 
as  the  surface  of  the  water  rises  in  the  vessel  F  G  the  actual 
leg  of  the  siphon  is  shortened.  When  the  surface  L  has  risen 
towards  the  level  of  the  surface  D,  then  the  legs  of  the  siphon 
become  equal,  and,  by  what  has  been  already  stated,  its  action 
must  cease. 


CHAP.    VI. 


SIPHONS. 


255 


It  thus  appears  that  the  siphon  is  merely  an  instrument  used 
in  decanting  a  liquid,  but  that  it  does  not  perform  the  office  of 
a  pump  in  raising  it  above  the  level  which  it  held  in  the  vessel 
from  which  it  is  drawn. 

The  process  of  exhausting  the  syringe  by  suction,  or  other- 
wise, is  frequently  difficult  and  always  inconvenient.  But  this 
may  be  avoided  by  presenting  the  legs  of  the  siphon  upwards 
in  the  first  instance,  and  having  stopped  the  shorter  leg  with 
the  hand,  filling  the  siphon  through  the  longer  leg  C  B.  Both 
ends  of  the  tube  being  then  stopped,  let  them  be  pressed  down- 
wards, the  shorter  leg  being  introduced  below  the  water  in  the 
cistern,  and  the  longer  leg  being  carried  over  the  vessel  in 
which  the  liquid  is  to  be  decanted. 

The  process  of  exhaustion  is  sometimes  facilitated  in  the 
following  manner : — A  small  tube  proceeds  from  the  longer 
leg  near  its  extremity  at  D,  fig.  44.  The  extremity  A  being 


immersed  in  the  liquid,  and  the  extremity  C  being  stopped  by 
the  hand,  the  mouth  applied  at  the  extremity  E  of  the  subsid- 
iary tube  will  exhaust  the  siphon  and  cause  the  water  to  rise 
in  it. 

When  the  siphon  is  constructed  upon  a  very  large  scale  this 
process  is  impracticable.  In  that  case  both  ends  of  the  tube  A 
and  C  may  be  first  plugged,  and  a  hole  being  made  at  the 
highest  part  B,  the  instrument  may  be  filled  with  liquid.  The 
hole  through  which  it  is  filled  being  then  plugged,  and  the 
extremities  opened,  the  instrument  will  act.  A  siphon  of  any 
magnitude  may  thus  be  constructed,  and  water  may  be  carried 
over  a  hill,  the  perpendicular  height  of  the  top  of  the  siphon 
not  exceeding  34  feet  above  the  level  of  the  reservoir  from 


256  A    TREATISE    ON    PNEUMATICS.  CHAP.    VI. 

which  the  water  is  to  be  drawn ;  but  it  is  obvious,  also,  that  the 
basin  into  which  it  is  discharged  must  not  be  higher  than  the 
level  of  the  receiver  from  which  it  is  drawn. 

The  Wurtemburg  siphon  has  the  convenience,  when  once 
filled,  of  always  remaining  so,  the  waste  by  evaporation  only 
being  supplied.  This  instrument  is  represented  in  Jig.  45» 

Fig.  45. 


When  not  in  use,  it  may  be  hung  up  upon  a  hook  or  nail  by 
the  curved  part  B.  The  ends  D  and  E  will  then  be  presented 
upwards,  the  liquid  being  retained  in  the  siphon  by  the  atmos- 
pheric pressure  acting  on  both  surfaces  at  D  and  E.  When 
the  leg  B  C  D  is  immersed  in  a  vessel  of  liquid,  the  surface  D 
is  pressed  clown  by  the  weight  of  the  incumbent  liquid,  and 
also  by  the  atmospheric  pressure  acting  above  that.  This 
pressure  is  transmitted  to  E,  where  it  is  resisted  by  the  atmos- 
pheric pressure  only  ;  consequently  the  Avater  will  be  driven 
from  E  with  a  force  equivalent  to  the  hydrostatic  pressure  on 
the  surface  D. 


CHAP.    VII.  AIR    GUN AIR    BALLOON.  257 

CHAP.    VII. 
THE  AIR  GUN,  AIR  BALLOON,  AND  DIVING  BELL. 

THE  AIR  GUN.— FIRST  ATTEMPTS  AT  BALLOONS.— LANA'S  BALLOON  OF 
RAREFIED  AIR,  —  FIRE  BALLOONS.—  MONTGQLFIER's  BALLOON. — 
FIRST  ASCENT. —  BALLOONS  INFLATED  WITH  HYDROGEN. — PARA' 
CHUTE. — BLANCHARD'S  EXPERIMENT.—  CAUSES  OF  THE  EFFICACY 

OF  THE  PARACHUTE.— ASCENT  OF  GAY  LUSSAC  AND  BIOT. — APPEAR- 
ANCES IN  THE  HIGHER  REGIONS  OF  THE  ATMOSPHERE. — THE 
DIVING  BELL. 

The  Jtir  Gun. 

(171.)  THE  air  gun  is  an  instrument  for  projecting  balls  or 
other  missiles  by  the  elastic  force  of  condensed  air. 

A  strong  *metal  ball  is  constructed,  furnished  with  a  small 
hole,  and  a  valve  opening  inwards  :  in  this  ball  air  may  be 
condensed  to  any  degree  which  its  strength  is  capable  of 
bearing,  by  means  of  a  condensing  syringe  screwed  into  the 
hole. 

When  this  condensation  has  been  accomplished,  the  ball  is 
detached  from  the  syringe  and  screwed  at  the  breech  of  a  gun, 
constructed  so  that  a  trigger  is  capable  of  opening  the  valve. 
The  ball  being  placed  in  the  barfel  near  the  breech,  and  fitting 
the  barrel  so  as  to  be  air-tight,  is  exposed  to  the  pressure  of 
the  condensed  air  the  moment  the  valve  is  opened :  this  pres- 
sure propels  it  along  the  barrel,  and  continues  to  act  upon  it  so 
long  as  the  valve -is  opened.  It  is  thus  projected  from  the 
gun  in  the  same  manner  as  that  in  which  a  ball  is  urged  by  the 
expansive  force  of  exploded  gunpowder.  The  force  of  projec- 
tion obviously  depends  on  the  degree  of  condensation  which  in 
given  to  the  air  in  the  ball. 

The  stock  of  the  gun  may  contain  a  magazine  of  balls,  and 
be  furnished  with  a  simple  mechanism  by  which  these  balls 
may  be  transferred  in  succession  into  the  barrel,  so  that  the  gun 
is  easily  and  quickly  loaded  after  each  discharge. 

The  magazine  of  condensed  air  may  receive  different  shapes 
and  be  differently  arranged  ;  but  that  which  is  now  described  is 
one  of  the  best  forms  for  it. 

The  Mr  Balloon. 

(172.)  The  physical  conditions  under  which  a  solid  body  im- 
mersed in  a  liquid  will  rise  to  the  surface,  sink  to  the  bottom, 

22* 


258  A    TREATISE    ON    PNEUMATICS.  CHAP.    VII. 

or  remain  suspended,  have  been  fully  detailed  in  a  former  part 
of  this  volume.  (Hydrostatics,  chap,  v.) 

If  a  body  be  heavier  than  the  quantity  of  liquid,  the  place  of 
which  it  occupies,  it  will  sink  by  that  preponderance.  If  it  be 
equal  in  weight  to  the  liquid  it  displaces,  it  will  remain  sus- 
pended, as  the  liquid  itself  would  ;  but  if  it  be  lighter  than  the 
liquid  which  is  displaced,  the  superior  weight  of  the  surround- 
ing liquid  will  press  it  upwards,  and  will  cause  it  to  ascend  to 
the  surface. 

Liquids  being  incompressible,  all  their  strata  have  the  same 
density,  or  nearly  so  ;  and,  consequently,  a  solid  which  at  one 
depth  is  lighter  than  the  liquid  which  it  displaces,  will  also  be 
lighter  at  every  depth.  Consequently,  if  a  solid  has  a  tendency 
to  rise  towards  the  surface  at  any  depth,  it  will  continue  so  to 
rise  until  it  reach  the  surface.  If,  however,  the  strata  of  liquid 
approaching  the  surface  had  gradually  decreased  in  density, 
then  the  solid,  which  was  lighter,  bulk  for  bulk,  than  an  inferior 
stratum,  might  be  equal  in  weight,  bulk  for  bulk,  to  a  superior 
one,  and  heavier,  bulk  for  bulk,  than  others  nearer  to  the  sur- 
face. Thus,  such  a  body  would  rise  at  certain  depths,  but  at 
other  lesser  depths  it  would  sink  ;  and  at  the  depth  of  a  certain 
stratum  it  would  remain  suspended. 

The  property  of  liquids,  which  is  the  cause  of  these  phe- 
nomena, is  their  power  of  freely  transmitting  pressure.  This 
will  be  plainly  perceived  by  referring  to  (55.),  where  it  is  shown 
that  the  solid  rises  to  the  surface  by  the  pressure  of  the  column 
of  the  liquid  whose  base  is  contiguous  to  it,  and  rests  on  the 
same  level,  and  which  pressure  is  transferred  to  the  base  of  the 
solid  by  the  inferior  strata  of  liquid.  Now  this  property  of 
transmitting  pressure  is  common  to  elastic  fluids,  and  we  are, 
therefore,  warranted  in  the  inference,  that  a  solid  suspended  in 
a  gaseous  fluid,  which  is  lighter,  bulk  for  bulk,  than  the  fluid, 
will  rise  ;  that  if  it  be  heavier,  bulk  for  bulk,  it  will  fall ;  and 
if  it  be  equal  in  weight,  bulk  for  bulk,  it  will  remain  suspended. 
That  a  solid,  therefore,  may  rise  in  the  atmosphere  with  any 
given  force,  it  13  only  necessary  lhat  its  weight  should  be  less 
than  the  weight  of  the  air  which  it  displaces  by  the  amount  of 
that  force.  Upon  this  principle  BALLOONS  are  constructed. 

The  method  of  constructing  a  balloon,  which  naturally  first 
suggests  itself,  is  to  exhaust  a  large  chamber  of  the  air  which 
it  contains,  so  as  to  render  it  a  vacuum,  or  nearly  so  :  it  v,  ill  then 
continue  to  displace  the  same  quantity  of  atmosphere  as  before, 
but  its  weight  will  be  diminished  by  the  weight  of  the  air  with- 
drawn from  the  chamber,  and  it  will  have  a  disposition  to  rise 
in  the  atmosphere  proportionate  to  the  difference  between  the 
actual  weight  of  the  materials  which  form  the  chamber  and  the 
weight  of  the  air  whose  place  it  occupies.  This  was,  accord- 


CHAP.  vii.       LANA'S  BALLOON.  259 

ingly,  the  method  adopted  in  the  earliest  attempts  on  record  to 
construct  balloons.  About  the  middle  of  the  seventeenth 
century,  a  Jesuit  named  Francis  Lana  constructed  four  hollow 
spheres  of  copper,  each  twenty  feet  in  diameter,  and  so  thin 
that  the  total  weight  of  the  copper  composing  them  was  less 
than  the  weight  of  the  air  which  they  would  displace. 

He  proposed  to  attach  these  spheres  to  a  boat  furnished  with 
a  sail,  as  represented  in  Jig.  46.,  by  which  means  he  hoped  to 
traverse  the  clouds. 

Fig.  46. 


The  method  of  exhaustion  which  Lana  possessed  was  insuf- 
ficient to  accomplish  his  purpose  ;  but  even  had.it  been  other- 
wise, the  atmospheric  pressure  acting  on  the  external  surface 
of  the  attenuated  metal  globes  would  have  crushed  them,  and 
proved  the  project  to  be  impracticable.  It  may  be  stated  gen- 
erally, that  no  known  solid  possesses  sufficient  strength  to 
enable  a  globe,  or  any  other  vessel  formed  of  it,  to  resist  the 
atmospheric  pressure  from  without,  when  that  pressure  is  not 
balanced  by  a  corresponding  pressure  from  within,  unless  it  be 
made  of  so  great  a  thickness  that  its  weight  will  very  much 
exceed  the  weight  of  the  air  which  it  displaces. 

To  give  sufficient  buoyancy  to  a  large  hollow  body,  and  at 
the  same  time  to  secure  it  from  the  effect  of  atmospheric  pres- 
sure, it  will  be  therefore  necessary  to  fill  it  with  some  elastic 
fluid  which  will,  by  its  elasticity,  balance  the  effect  of  the  ex- 


260 


A    TREATISE    ON    PNEUMATICS. 


CHAP.    VII. 


ternal  air,  and,  by  its  small  specific  weight,  produce  a  degree 
of  buoyancy  sufficient  to  raise  the  materials  of  which  it  is 
constructed.  In  this  case,  as  the  forces  which  act  on  the  bal- 
loon are  held  in  a  state  of  equilibrium,  or  nearly  so,  no  extraor- 
dinary degree  of  strength  is  required,  and  any  extremely  light 
and  flexible  substance  impervious  to  air  or  gas  may  be  used. 

The  most  obvious  contrivance  which  is  suggested  by  these 
considerations  is  atmospheric  air  rarefied  by  heat ;  for  in  this 
case,  the  expansion  produced  by  the  heat  gives  the  same  degree 
of  elasticity  with  a  much  less  quantity  of  atmospheric  "air. 
To  explain  this,  let  a  glass  bulb  A  be  furnished  with  a  tube  T, 
which,  rising  from  it  to  the  extremity  at  which  it  is  curved, 
descends  into  a  vessel  V,  fig.  47.,  containing  water  or  other 

Fig.  47. 


liquid  :  the  air  is  thus  enclosed  in  the  tube  in  the  common  state 
of  the  external  atmosphere.  Let  a  spirit  lamp,  or  any  other 
source  of  heat,  be  now  applied  to  the  bulb  at  A  ;  the  air  in  the 
bulb,  receiving  increased  elasticity  from  the  heat,  will  press  the 
water  towards  the  mouth  of  the  tube,  and,  rising  in  bubbles, 
will  escape  at  the  surface  of  the  water.  This  will  continue 
until  the  air  in  the  tube  is  highly  rarefied  ;  still,  however, 
retaining  a  degree  of  elasticity  sufficient  to  balance  the  atmos- 
pheric pressure  acting  on  the  surface  of  the  water  in  the 
vessel,  and  transmitted  by  it  to  the  surface  of  the  water  in  the 
tube.  That  the  air  in  the  tube  is  highly  rarefied,  may  be  veri- 
fied by  removing  the  lamp  from  the  bulb :  as  the  tube  cools,  the 
air  will  contract  itself  into  its  former  dimensions,  and  the 
pressure  of  the  atmosphere  will  force  the  liquid  through  the 


CHAP.    VII.  FIRE    BALLOON.  261 

mouth  of  the  tube  and  over  the  curved  part  into  the  bulb.  It 
will  bo  found,  that  in  this  way  the  bulb  and  tube  will  be  filled, 
with  the  exception  of  a  very  small  bubble  of  air,  which  will 
remain  suspended  at  the  highest  point  of  the  tube  :  this  bubble 
will  have  the  same  temperature  as  the  external  air,  and  the 
same  pressure  ;  and  it  is  obvious,  that  this  is  as  many  times 
lighter  than  the  air  which  originally  filled  the  tube  and  bulb,  as 
its  present  magnitude  is  less  than  the  whole  contents  of  the 
bulb  and  tube. 

If,  instead  of  a  glass  bulb,  we  take  a  large  spherical  bag  con- 
structed of  any  light  substance,  and  having  in  one  part  a  circular 
opening  or  hole,  this  bag  may  be  distended  by  blowing  into  it 
common  air.  If  the  hole  be  then  presented  downwards,  and  a 
lamp  suspended  beneath  it,  the  flame  of  the  lamp  will  gradually 
increase  the  temperature  of  the  air  contained  in  the  bag :  it 
will  thus  acquire  increased  elastic  force,  by  which  a  part  will 
be  expelled  at  the  hole  under  which  the  lamp  is  suspended. 
This  process  of  rarefaction  will  be  continued  so  long  as  the  air 
contained  in  the  bag  receives  increased  temperature  from  the 
heat  of  the  lamp  ;  but  throughout  the  whole  process  the  elastic 
force  of  the  rarefied  air  will  be  equal  to  the  external  pressure 
of  the  atmosphere,  and  the  bag  will  be  subject  to  no  force  tend- 
ing either  to  burst  it  or  to  crush  it. 

Such  a  bag,  if  constructed  of  sufficient  magnitude,  may  by 
these  means  be  rendered  lighter  than  the  air  which  it  displaces. 
It  will  thus  have  a  corresponding  buoyancy,  and  will  ascend  in 
the  atmosphere  with  a  force  equal  to  the  difference  between  its 
own  weight  and  the  weight  of  the  air  which  it  displaces. 

The  application  of  these  principles  forms  the  first  successful 
attempt  in  aeronautics.  In  the  year  1782,  two  paper-makers, 
named  Montgolfier,  residing  at  Annonai,  in  France,  constructed 
a  bag  of  silk,  in  the  form  of  a  square  box,  containing  about  40 
solid  feet  when  filled.  In  the  bottom  of  this  was  placed  an 
aperture,  under  which  burning  paper  was  applied :  it  ascended 
to  nearly  100  feet  in  the  air.  The  experiment  was  immediately 
instituted  on  a  larger  scale.  A  balloon,  constructed  of  a  capaci- 
ty exceeding  700  solid  feet,  rose  in  the  same  manner  to  an 
elevation  of  more  than  600  feet.  A  balloon  in  the  spherical 
form,  but  on  a  scale  still  larger,  was  next  constructed  ;  it  con- 
tained 23,000  feet,  and  had  a  buoyancy  capable  of  raising  500 
pounds.  It  ascended  in  the  atmosphere  to  a  height  of  about 
6000  feet. 

Hitherto  the  experiments  were  confined  to  the  object  of 
ascertaining,  the  mere  possibility  of  ascending  in  the  atmos- 
phere ;  and,  in  some  cases,  the  effects  produced  on  animal 
life  at  great  elevations  were  tried,  by  sending  up  various  ani 


A    TREATISE    ON    PNEUMATICS.  CHAP.    VII. 


°f  wicker-work  suspended  from  the 
At  length,  in  the  latter  end  of  the  year  1783,  a  balloon  was 

t^™'  Wlth  a  Vlew  to  transP°rt  one  or  more  pe> 
the  higher  regions  of  the  atmosphere.     This  machine 

3!     °f  ^  f^  ^  74  *<*  in  height  and  48  in 
Immediately  under  an  aperture  in  the  bottom  of  the 

onSPen?ed  ^r11  gmte  Wlthin  reach  of  the  aeronaut! 
Son  w?h'Watl  Pf  if  the  bUrning  fuel  to  maintain  the  rare^c- 
abourSOOO  ft  h  M°P'I  An/s'ent  was  ™de  to  a  height  of 
bout  3000  feet  by  M.  Pilatre  de  Rozier  and  the  marquis  d'Ar- 
landes.  After  this  experiment  various  others  succeeded  in 
balloons  constructed  in  the  same  manner 

maThinP^xlf  -TCit0r  °f  theS6  balloons  conceived  that  the 
machine  owed  its  buoyancy  to  the  gas  produced  by  the  fire, 
and  which  with  an  elastic  pressure  equal  to  the  air  was  sped?' 
M^&;  S  6  mechanical  PfinciPle  of  the  ascenrwas 

The  step  from  fire  balloons  to  balloons  filled  with  gas  specif- 
ically  hghter  than  atmospheric  air,  of  the  same  preL^wi 
now  easy  and  obvious.  The  gas  at  present  denominated 
hydrogen  was  submitted  to  a  series  of  experiments,  by  which 
t  was  found  that  its  specific  gravity  was  only  one  seventh  of 

it  ot  common  atmospheric  air.  It  was  obvious,  therefore, 
that  a  balloon  filled  with  this  gas  would  have  considerable 

oyaney.     Balloons  were  accordingly  constructed  and  inflated 
.  tnis  gas,  and  various  ascents  have  since  been  made  the 
particulars  of  which  would  not  be  suitable  to  the  limHs  of  the 
present  treatiss 

The  density  of  each  stratum  of  air  being  proportional  to  the 

pressure  under  which  it  is  placed,  it  followsthat  in  ascending 

i  the  atmosphere  the  strata  will  have  less  and  less  specifif 

tghP  In7'       f    f       M'I  fcerefore,  containing  gas  which  balances 

the  lower  strata,  will,  if  it  be  completely  filled,  have  a  tendency 

st  when  it  has  ascended  into  the  higher  strata  :  for  the 

gas,  not  having  room  to  expand,  will  maintain  its  original  elastic 

ce  whi  e  the  atmospheric  pressure,  being  diminished  in  the 

ascent  will  cease  to  balance  this  elastic  force  of  the  confined 

There  will  then  be  a  bursting  pressure  equivalent  to  the 

ess  of  the  atmospheric  pressure  of  the  lower  strata  over  the 

aosphenc  pressure  in  the  strata  to  which  the  balloon  has 
ascended. 

tfe^T  eff^ct\maj  be  Provided  against  by  imperfectly  filling 

the  balloon  in  the  first  instance,  so  that  as  it  ascends,  the  ga? 

which  it  contains  will  have  room  to  expand,  and  thus,  while  the 

sure  of  the  atmosphere  is  diminished,  the  elastic  pressure 


CHAP.  VII.  HYDROGEN    BALLOONS. 


of  the  gas  in  the  balloon  will  be  diminished  in  the  same  propor- 
fhS'dp  lon^a\ the  atmospheric  pressure  is  not  diminished  to 
that  degree  which  would  cause  the  gas  enclosed  in  the  balloon 

buSh  hSliaS  t0  comPlet&  inflate  ^  no  force  tending  to 
burst  the  balloon  can  exist ;  but  should  the  ascent  be  continued 
to  a  greater  height,  then  a  bursting  pressure  will  be  called  into 
action  by  the  pressure  of  the  atmosphere  being  diminished  in  a 
greater  degree  than  the  elastic  force  of  the  g!s  in  the  balloon 
In  this  case  the  danger  may  be  removed  by  the  provision  of  a 
valve  opening  in  some  convenient  part  of  the  balloon,  by  which 
a  part  of  the  gas  may  be  allowed  to  escape.  Such  a  valve  is 
also  necessary  in  order  to  enable  the  aeronaut  to  descend  at 
pleasure.  Without  it  he  would  be  compelled  to  remain  in  the 
atmosphere  as  long  as  the  balloon  continued  to  retain  the  gas 
with  which  it  was  inflated  ;  but  provided  with  such  a  valve,  he 

^m  ^n^f'rf  ^  gaS  ^  escaP^  and  thereby  diminish 
ie  magnitude  of  the  balloon,  and  consequently  produce  a  cor- 
responding  decrease  in  its  buoyancy. 

By  analogy  we  should  infer  that  the  power  of  ascending  at 
p  easure  would  be  obtained  by  being  able  to  supply  an  increased 
quantity  of  gas  to  the  balloon;  but  this  would  not  be  easily 

obtain^  h  5  '  accordin^'the  power  of  ascending  has  been 
obtained  by  carrying  up  sand-bags,  or  other  weights  called 
ballast,  by  throwing  out  which  the  machine  is  lightened,  and 

fonnH  t  fT '"I5  7  lf  fr°m  any  accidental  cause  it  should  be 
found  to  fall  with  dangerous  precipitancy,  its  rate  of  descent 
may  be  retarded  by  throwing  out  this  ballast. 

nJ«Eff!S£  CTe  °f  d??ger  attendin£  aeronautical  experi- 
ments arises  from  the  accidental  escape  of  the  gas  from  the 
balloon;  and  it  has  consequently  been  a  desirable  object  to 
itrive  means,  m  such  cases,  for  rendering  the  fall  of  the 
aeronaut  less  liable  to  dangerous  effects.  With  this  view  an 
apparatus  has  been  contrived,  called  a  parachute.  It  is  usually 
formed  like  a  large  umbrella,  which  spreads  above  the  car  with 
its  concave  side  presented  downwards.  The  effect  of  this 
acting  against  the  air  below  is  to  break  the  descent,  and  after 
a  short  time  the  rate  of  descent  becomes  uniform,  instead  of 
£££™  y  r°  1G8  £enerally  are>  accelerated.  The  magni- 
tude of  the  parachute  may  be  such,  that  the  rate  of  descent  shall 
>e  so  slow  that  no  danger  is  to  be  apprehended  from  the  con- 
cussion attending  the  fall.  If,  therefore,  the  aeronaut  descend 
on  land,  his  safety  is  insured. 

The  subjects  of  the  first  experiments  with  the  parachute  were 
naturally  inferior  animals.  M.  Blanchard  dropped  a  dog  sus- 
pended from  a  parachute,  from  the  altitude  of  6000  feet  above 
the  surface  of  the  earth.  A  whirlwind  interrupted  its  descent, 
and  carried  it  above  the  clouds.  The  aeronaut  soon  after  met 


264  A    TREATISE    ON    PNEUMATICS.  CHAP.    VII. 

the  parachute  again ;  the  dog  recognized  its  master,  and  express- 
ed his  uneasiness  and  solicitude  by  barking ;  another  current  of 
air,  however,  carried  him  off,  and  he  was  lost  sight  of.  The 
parachute  with  the  dog  descended  soon  after  the  aeronaut  in 
safety.  Ten  years  after  this,  M.  Garnerin  made  several  suc- 
cessful experiments  with  the  parachute.  He  placed  it  half 
expanded  between  the  balloon  and  the  car,  so  as  to  spread  like 
an  umbrella  above  him.  At  the  height  of  about  2000  feet  he 
had  the  intrepidity  to  cut  off  the  parachute  and  car  from  the 
balloon.  He  descended  slowly,  the  parachute  gradually  unfold- 
ing itself,  and  finally  reached  the  ground  in  safety.  The  same 
experiment  was  several  times  repeated  with  similar  success. 
In  one  case  he  descended  from  the  perpendicular  height  of  8000 
feet. 

As  the  balloon  derives  its  efficacy  from  the  weight  of  the 
atmosphere,  the  parachute  depends  on  the  inertia  of  that  fluid. 
In  descending,  the  broad  concave  surface  of  the  parachute  must 
drive  before  it  the  column  of  air  extending  from  its  surface  to 
the  ground  ;  but  the  circumstance  on  which  its  principal  excel- 
lence depends  is,  that  the  resistance  arising  from  this  inertia 
increases  in  a  more  rapid  proportion  than  the  velocity  of 
descent.  A  double  velocity  in  the  parachute  would  produce  a 
fourfold  resistance  in  the  ait ;  a  threefold  velocity  would  pro- 
duce a  ninefold  resistance  ;  a  fourfold  velocity  a  sixteenfold 
resistance ;  and  so  on.  The  law  of  this  resistance  has  been 
already  fully  explained  respecting  liquids  in  (107.) ;  and  it  may 
be  explained  in  the  case  of  the  atmosphere  in  exactly  the  same 
words  ;  but  in  the  case  of  the  descent  of  the  parachute  from 
great  elevations,  there  is  an  obvious  cause  which  makes  the 
resistance  increase  even  in  a  more  rapid  proportion  than  is 
indicated  by  this  law.  The  increase  of  the  resistance  in  the 
proportion  of  the  square  of  the  velocity  arises  from  the  suppo- 
sition that  the  resisting  fluid  through  which  the  body  moves 
continues  to  be  of  the  same  density.  Now  this  is  not  the  case 
with  the  atmospheric  air  through  which  the  parachute  falls  ; 
each  stratum  into  which  it  enters  has  a  density  greater  than 
that  from  which  it  descends,  and  consequently,  on  that  account 
alone,  will  offer  a  proportionally  increased  resistance.  This 
cause,  added  to  the  former,  will  very  speedily  compel  the  para- 
chute to  descend  with  a  uniform  velocity.  This  velocity  will 
be  small  in  the  same  proportion  as  the  parachute  is  large,  and 
as  the  weight  of  the  car  and  its  contents  is  small. 

As  the  gas  by  which  a  balloon  is  inflated  is  lighter  than  the 
atmosphere,  the  valve  provided  for  its  escape,  when  the  aero- 
naut wishes  to  descend,  is  placed  usually  in  the  top  of  the 
balloon.  If  it  were  placed  in  the  bottom,  even  although  it  were 
open,  the  gas  would  not  escape  ;  at  least  not  in  any  considera- 


CHAP.  VII.  PARACHUTES.  265 

ble  quantity,  nor  with  any  degree  of  certainty.  The  superior 
pressure  of  the  atmosphere,  and  the  natural  levity  of  the  gas 
itself,  would  prevent  its  escape  ;  but  when  the  valve  is  placed 
in  the  top,  the  gas  will  issue  from  it  on  the  same  principle  as  a 
lighter  fluid  rises  in  a  heavier.  The  car  which  bears  the  aero- 
naut is  usually  supported  by  a  net-work,  which  extends  over 
the  balloon  and  which  is  connected  with  it  by  a  number  of  ropes 
and  strings,  as  represented  in  Jig.  48. 

Fig.  48. 


The  total  impracticability  of  guiding  or  governing  balloons 
in  their  course  through  the  air,  has  hitherto  prevented  them 
from  being  applied  to  any  purpose  of  extensive  utility.  Scien- 
tific men  have,  on  some  occasions,  ascended  in  the  atmosphere, 
with  a  view  of  observing  at  great  elevations  the  effect  of  tem- 
perature, pressure,  electricity,  and  other  phenomena  connected 
with  meteorology.  In  1804,  M.  Gay  Lussac  and  M.  Biot  made 
an  ascent  from  Paris,  furnished  with  various  meteorological 
apparatus,  to  a  height  of  upwards  of  13,000  feet.  Soon  after- 
wards, M.  Gay  Lussac  ascended  alone,  to  a  height  of  23,000 
feet  above  Paris.  In  1807,  M.  Garnerin  ascended  at  ten  o'clock 
at  night  from  Paris,  and,  rising  with  unusual  rapidity,  soon 
attained  an  immense  elevation  above  the  clouds.  By  some 
neglect,  the  apparatus  for  discharging  the  gas  from  the  balloon 


266  A  TREATISE  ON  PNEUMATICS.  CHAP.    Vlt. 

was  found  to  be  unmanageable,  and  the  high  degree  of  rare- 
faction  at  so  great  an  elevation  produced  in  the  balloon  such  a 
tendency  to  burst,  that  the  aeronaut  was  obliged  to  cut  a  hole 
in  the  silk  to  allow  the  escape  of  the  air.  The  .balloon  then 
descended  with  such  rapidity,  that  he  was  obliged  to  counteract 
its  motion  by  casting  out  all  his  ballast.  The  balloon  thus 
continued  alternately  rising  and  sinking  for  nearly  eight  hours, 
during  which  he  experienced  the  effects  of  a  thunder  storm,  by 
which  he  was  finally  dashed  against  the  mountains.  He  landed 
at  Mont  Tonnere,  at  a  distance  of  300  miles  from  Paris. 

The  effects  produced  on  the  aeronaut  by  the  rarefaction  of 
the  atmosphere  at  great  elevations,  are  sensibly  manifested  in 
respiration  ;  the  pulse  is  rendered  more  rapid,  the  head  unusu- 
ally swelled,  and  the  throat  parched. 

The  intense  cold  which  also  necessarily  accompanies  rare- 
faction produces  great  inconveniences,  and  an  irresistible 
disposition  to  sleep  is  felt 

It  has  been  found  also  that  storms  and  currents  in  the  atmos- 
phere are  local,  and  that  while  one  stratum  is  thus  agitated, 
other  strata  inferior  or  superior  to  it  will  be  calm.  By  man- 
aging his  ascent  or  descent,  the  aeronaut  may  thus  transfer  him- 
self from  wind  to  stillness,  from  a  storm  to  a  calm,  or  from  one 
current  of  wind  to  another  in  a  different  direction.  The  veloci- 
ty with  which  balloons  are  sometimes  transported  through  the 
air  amounts  to  eighty  miles  an  hour.  The  appearance  of  the 
clouds  from  great  heights  is  said  to  resemble  a  plain  of  snow, 
or  a  sea  of  white  cotton.  Those  which  are  charged  with  elec- 
tricity are  said  to  resemble  the  smoke  of  ordnance.  Clouds 
containing  hail  or  snow  are  often  encountered,  in  which  the  car 
becomes  almost  filled  with  these  substances.  Clouds  of  mist 
or  rain  frequently  drench  the  aeronaut.  When  birds  are  allow- 
ed to  escape  from  the  balloon  at  a  great  height,  they  fall  almost 
perpendicularly  downwards,  the  attenuated  air  not  having  suffi- 
cient inertia  to  offer  resistance  to  their  wings.* 

Attempts  have  been  made  to  render  balloons  useful  in  mili- 
tary operations,  by  viewing  from  an  elevated  position  the  dispo- 
sition and  movements  of  an  hostile  army.  An  academy,  with 
this  object,  was  actually  established  at  Neudon,  near  Paris, 
during  the  late  war,  where  a  corps  of  aeronauts  was  trained  to 
the  service.  A  balloon  was  kept  constantly  inflated^  and 
secured  to  the  ground  by  a  rope,  which  allowed  it  to  ascend  to 
a  height  of  about  twenty-five  yards.  At  this  institution  military 
balloons  were  prepared  for  the  different  divisions  of  the  French 
army  •  and  on  one  occasion  an  ascent  was  made  by  a  French 
general,  at  the  battle  of  Fleury,  to  a  height  of  nearly  500  yards, 

*  The  Edinburgh  Encyclopaedia,  article  Aeronautics. 


CHAP.    VII.  DIVING    BELL.  267 

from  which  he  reconnoitred  the  hostile  armies.  It  is  said  that 
the  signals  which  were  made  to  general  Jourdan  on  this  occa- 
sion decided  the  fate  of  the  engagement.  The  project,  however, 
has  long  since  been  abandoned,  not  being  found  generally 
available. 

It  has  been  proposed  to  render  balloons  useful  in  geographi- 
cal surveys,  both  as  a  means  of  raising  the  observer  to  great 
elevations,  and  of  transmitting  signals  to  great  distances. 

The  Diving  Bdl 

(173.)  The  spirit  of  inquiry  which  so  strongly  characterizes 
the  human  mind,  and  which  stimulates  man  to  undertakings  in 
which  life  itself  is  imminently  risked,  has  not  only  prompted 
him  to  ascend  into  the  regions  of  the  air,  but  has  also  carried 
him  to  the  depths  of  the  sea. 

The  practice  of  diving  is  of  very  early  origin,  and  was  first 
probably  adopted  for  the  recovery  of  articles  of  value  dropped 
into  the  water  at  small  depths.  Instances  are  recorded  of  per- 
sons having  acquired  by  practice  the  habit  of  enduring  submer- 
sion for  a  length  of  time  which  in  many  cases  seems  astonishing, 
and  in  others  altogether  incredible.  Indeed,  the  circumstances 
attending  most  of  these  narrations  bear  unequivocal  marks  of 
fiction.  The  gratification  of  a  taste  for  the  marvellous  does  not 
tempt  us  to  allow  a  space  in  our  pages  for  a  description  of  the 
feats  of  the  Sicilian  diver,  whose  chest  was  so  capacious  that  by 
one  inspiration  he  could  draw  in  sufficient  air  to  last  him  a  whole 
day,  during  which  time  he  would  sojourn  at  the  bottom  of  the 
sea,  and  who  became  so  inured  to  the  water,  that  it  was  almost 
a  matter  of  indifference  to  him  whether  he  walked  on  dry  land 
or  swam  in  the  deep,  remaining  often  for  five  days  in  the  sea 
living  upon  the  fish  which  he  caught ! 

Various  attempts  were  made  to  assist  the  diver  by  enabling 
him  to  carrv  down  a  supply  of  air  ;  and  after  a  long  period  and 
gradual  improvements,  suggested  by  experience,  the  present 
diving  bell  was  produced. 

This  machine  depends  for  its  efficacy  on  that  quality  in  air 
which  is  common  to  all  material  substances,  impenetrability  ; 
that  is,  the  total  exclusion  of  all  other  bodies  from  the  space  in 
which  it  is  present.  The  diving  bell  is  a  large  vessel  closed  at 
the  sides  and  at  the  top,  but  open  at  the  bottom.  It  should  be 
perfectly  impenetrable  to  air  and  water.  When  such  a  machine, 
with  its  mouth  downwards,  is  pressed  into  the  water  by  sufficient 
weights  suspended  from  it,  the  air  contained  in  it  at  the  surface 
will  be  enclosed  by  the  sides,  the  top,  and  the  surface  of  the  water 
which  enters  the  mouth  of  the  machine.  As  it  descends  in  the 


268  A    TREATISE    ON    PNEUMATICS.  CHAP.   VII. 

liquia,  tne  air  enclosed  in  it  is  subject  to  the  pressure,  which 
increases  in  proportion  to  the  depth,  and  by  virtue  of  its  elas- 
ticity will  become  condensed  in  proportion  to  this  pressure. 
Thus  at  the  depth  of  about  34  feet,  the  hydrostatic  pressure 
will  be  equal  to  that  of  the  atmosphere  ;  and  since  the  air  at 
the  surface  of  the  water  is  under  the  atmospheric  pressure,  it 
will  be  affected  by  double,  the  pressure  at  the  depth  of  34  feet. 
It  will,  therefore,  conformably  to  what  was  explained  in  (132.), 
be  condensed  so  much  as  to  be  reduced  to  half  its  original 
dimensions.  Half  the  capacity  of  the  machine  will,  therefore, 
be  filled  with  water,  and  the  other  half  will  contain  all  the  air 
which  filled  the  machine  at  the  moment  of  its  immersion.  As 
the  depth  is  increased,  the  space  occupied  by  the  air  in  the  bell 
will  be  proportionably  diminished. 

It  is  well  known  that  if  an  animal  continue  to  respire  in  a 
space  from  which  a  fresh  supply  of  atmospheric  air  is  excluded, 
the  air  confined  in  the  space  will  at  length  become  unfit  for  the 
support  of  life.     This  is  owing  to  an  effect  produced  upon  the 
air  drawn  into  the  lungs,  by  which  when  breathed  it  contains 
carbonic  acid,  an  ingredient  not  present  in  the  natural  atmos- 
phere, and  which  is  highly  destructive  to  animal  life.*     When 
the  air  in  which  the  animal  is  confined  has  been  breathed  for  a 
length  of  time,  this  effect  being  repeated,  the  air  enclosed 
becomes  highly  impregnated  with  this  gas ;  and  if  its  escape  be 
not  allowed,  and  a  fresh  supply  of  atmospheric  air  admitted,  the 
animal  cannot  live.     If,  therefore,  a  diving  bell  be  used  to  ena- 
ble persons  to  descend  in  water,  it  will  be  necessary  either  to 
raise  them  to  the  surface  after  that  interval  in  which  the  air 
confined  in  the  bell  becomes  unfit  for  respiration,  or  means  must 
be  adopted  to  send  down  a  supply  of  fresh  air,  and  to  allow  the 
impure  air  to  escape.     But  besides  this,  there  is  another  reason 
why  means  of  sending  down  a  supply  of  air  are  necessary.    It 
has  been  already  proved,  that  the  hydrostatic  pressure  causes 
the  water  to  fill  a  large  part  of  the  capacity  of  the  machine,  the 
air  contained  in  it  being  condensed.     It  is  necessary,  therefore, 
in  order  to  maintain  sufficient  room  for  the  diver  free  from  water, 
to  supply  such  a  quantity  of  air,  as  that  in  its  condensed  state 
it  will  keep  the  surface  of  the  water  near  the  mouth  of  the 
machine.     Thus,  at  the  depth  of  34  feet,  it  will  be  necessary 
to  supply  as  much  air  as  would  fill  the  bell  in  its  natural  state. 
At  double  that  depth,  as  much  more  will  be  necessary,  and 
so  on. 

*  There  is  always  present,  however,  in  every  part  of  the  atmosphere,  a  very 
small  and  variable  proportion  of  carbonic  acid.  Animal  respiration  greatly  in- 
creases the  quantity  of  this  deleterious  gas  in  a  confined  portion  of  air,  and  also 
diminishes  the  quantity  of  oxygen  gas,  that  constituent  of  atmospheric  air  OB 
which  its  power  of  iustaining  life  depends. — AM.  ED. 


CHAP.    VII.  DIVING    BELL.  269 

The  air  necessary  for  these  purposes  is  supplied  by  one  or 
more  large  condensing  syringes,  constructed  on  the  principle 
explained  in  (162.).  These  syringes,  or  pumps,  are  placed  above 
the  surface  of  the  water  into  which  the  bell  is  let  down,  and 
they  communicate  with  the  interior  of  the  bell  by  a  flexible  tube 
carried  through  the  water  and  under  the  mouth  of  the  bell. 
Through  this  tube  any  quantity  of  fresh  air,  which  may  be 
requisite  for  either  of  the  purposes  already  mentioned,  may 
be  supplied.  A  tube  furnished  with  a  stopcock  is  placed  in  the 
top  of  the  bell,  by  which  the  diver  can  let  any  quantity  of 
impure  air  escape,  to  make  room  for  the  fresh  air  which  is 
admitted.  The  impure  air  will  rise  by  its  levity  in  bubbles  to 
the  surface.  i 

The  diving  bell  received  its  name  from  the  shape  originally 
given  to  it.  It  was  constructed  with  a  round  top,  increasing  in 
magnitude  towards  the  mouth,  thus  resembling  the  shape  of  a 
bell.  It  is  now,  however,  usually  constructed  square  at  the  top 
and  bottom,  the  bottom  being  a  little  larger  than  the  top,  and 
the  sides  slightly  diverging  from  above.  The  material  is  some- 
times cast  iron,  the  whole  machine  being'  cast  in  one  piece, 
and  made  very  thick,  so  that  there  is  no  danger  either  from 
leakage  or  fracture.  In  this  case  the  weight  of  the  machine 
itself  is  sufficient  to  sink  it.  Diving  bells,  however,  are  also 
sometimes  constructed  of  close-grained  wood,  two  planks  being 
connected  together  with  sheet  lead  between  them. 

In  the  top  of  the  machine  are  placed  several  strong  glass 
lenses  for  the  admission  of  light,  such  as  are  used  in  the  decks 
of  vessels  to  illuminate  the  apartments  below. 

The  shape  of  the  machine  is  generally  oblong,  with  seats  for 
the  diver  at  the  end ;  shelves  for  tools,  writing  materials,  or  any 
other  articles  necessary  to  be  carried  down,  are  placed  at  the 
sides  ;  and  below  the  seats  there  are  boards  placed  across  the 
machine  to  support  the  feet.  Messages  are  communicated  frona 
below  to  above  either  in  writing  or  by  signals.  A  board  is  car- 
ried in  the  bell  on  which  a  written  message  may  be  chalked. 
This  board  communicates  by  a  cord  with  the  arm  of  the  super- 
intendent above,  who,  on  a  signal  given,  draws  it  up,  and  who, 
in  a  similar  way,  is  able  to  return  an  answer. 

When  the  bell  is  of  cast  iron,  a  system  of  signals  may  be 
made  by  very  simple  means ;  a  blow  struck  by  a  hammer  on  the 
bell  produces  a  peculiar  sound  distinctly  audible  at  the  surface 
of  the  water,  arid  which  cannot  be  mistaken  for  any  other  noise. 
The  number  of  strokes  made  on  the  bell  indicate  the  nature  of 
the  message,  the  smaller  number  of  strokes  signifying  those 
messages  most  frequently  necessary.  Thus,  a  single  stroke 
calls  for  a  supply  of  fresh  air  ;  two  strokes  command  the  bell  to 
stand  still ;  three  express  a  desire  to  be  drawn  up  ^  four  to  b« 
23* 


270  A    TREATISE    ON    PNEUMATICS.  CHAP.    VII. 

lowered,  and  higher  numbers  express  motion  in  different  direc- 
tions. Of  course  this  system  of  signals  is  arbitrary,  and  liable 
to  be  varied  in  different  places. 

The  bell  is  usually  suspended  from  a  crane,  which  is  placed 
above  the  surface  of  the  water ;  and  in  order  to  move  it,  this 
crane  is  placed  on  a  railway,  by  which  it  is  enabled  to  traverse 
a  certain  space  in  one  direction.  The  carriage  which  traverses 
this  railway  supports  another  railway  in  directions  at  right 
angles  to  it,  on  which  the  crane  is  supported.  By  these  means 
two  motions  may  be  given  to  the  crane,  the  extent  of  which 
may  be  determined  by  the  length  of  the  railway,  and  the  bell 
may  be  brought  to  any  part  of  the  bottom  which  is  perpendicu- 
larly below  the  parallelogram  formed  by  the  length  of  the 
railway. 


INDEX. 


A. 

Adulteration  of  milk  ;  of  spirits,  page 

126. 
Air,  its  color,  175 ;    has  weight,  176 ; 

the  effects  of  its  inertia,  177  ;  proofs 

of  its  materiality  ;  impenetrable,  178 ; 

its  elasticity ;  its  elasticity  explained, 

181. 

Air-pump,  223 ;  experiments  with,  229, 
Air-vessel  of  forcing-pumps,  248. 
Air-balloon,  257. 
Air-gun,  257. 
Alloys,  123. 

Amazon,  river,  its  disappearance,  48. 
Animals,  birds,  and  fishes,  their  shape 

explained,  147. 
Archimedes,  his  experiment  on  Hiero's 

crown,  126  ;  his  screw,  157. 
Aristotle,  his  knowledge  of  the  weight 

of  air,  190. 
Arlandes,  Marquis  de,  his  ascent  in  a 

balloon,  262. 

Atmosphere,  its  probable  limits,  182. 
Atmospheric  air,  its  properties,   174 ; 

its  elasticity  equal  to  its  weight,  187 ; 

its  height,  205;    its  pressure,  205; 

pressure  bursts  a  bladder,  229  ;  effects 

in  the  higher  strata  observed  in  bal- 
loons, 266. 

B. 

Balance,  hydrostatic,  116. 

Ballast,  its  effect  in  ships,  99. 

Ballcock  ej:plaincd,  77. 

Balloons,  air,  257  ;  formed  of  air  rare- 
fied by  heat,  260';  Montgolfier's,  261 ; 
Pilatro  de  Rozier's  ascent ;  Marquis 
do  Arlandes's  ascent;  first  inflated 
with  hydrogen,  262 ;  Blanchard's  as- 
cent, 263 ;  ascents  of  Gay-Lussac, 
Biot,  and  Garnerin,  265;  their  military 
use,  266. 

Barker's  mill,  156. 

Barometer  discovered  by  Torricelli,  190. 
applied  to  the  measurement  of  heights 
by  Pascal,  191 ;  construction  of,  192  ; 
diagonal,  197  ;  wheel,  198  ;  its  uses  ;  a 
weather  glass, 201 ;  measuring  heights 
by,  203. 

Bellows,  hydrostatic,  12;  domestic  forge, 
208. 

Birdcage  fountain,  211. 

Birds  ;  their  flight  depends  on  air,  178. 


Blanchard,  his  ascent  in  a  balloon,  263. 
Boiling  water,  the  process  of,  85. 
Bramah,  his  press,  10. 
Breathing  accounted  for,  207. 
Buoyancy  explained,  74. 

C. 

Camel  for  lifting  vessels  over  shoals, 

78. 
Campbell,  his  experiment  on  a  bottle 

sunk  in  the  sea,  34. 
Canals,  construction  of,  49 ;  locks  of, 

49  ;  their  defect  as  means  oftransport, 

148. 

Cataracts,  their  heights,  47. 
Chain  pump,  165. 
Cities,  method  of  supplying  them  with 

water,  37.  51. 

Clocks,  ornamental  fountain,  46. 
Color  of  air,  174. 
Compressibility,  172. 
Condenser,  237. 
Condensing  syringe,  234. 
Contrivance  to  prevent  foundering,  76. 
Cream  floats  on  milk,  84. 
Cupping,  233. 

D. 

Dectot,  his  hydreoles,  90. 

Density,  109. 

De  Parcieux's  hydrometer,  122. 

Diagonal  barometer,  197. 

Discovery  of  atmospheric  pressure,  its 

history,  188. 

Diver,  effect  upon,  at  great  depths,  35. 
Diving  bell,  267. 
Double  forcing  pump,  250. 


Elasticity  of  air,  170  ;  proportional  to 
its  density,  182;  of  atmosphere  equal 
to  its  weight,  187  ;  of  air  bursts  a 
bladder,  229. 

Engine,  fire,  251. 

Exhausting  syringe,  215. 


Fire  engine,  251. 

Fish,  their  power  of  rising  and  sinking, 
'   81 

Flies,  their  power  of  walking  on  ceil- 
ing?, 207. 


272 


INDEX. 


Floating  bodies,  their  position  ;  equilib- 
rium of,  91 ;  on  water  explained,  79 ; 
bodies  explained,  71. 

Forcing  pump,  246 ;  double,  250. 

Fountains,  natural  ones  explained,  47  ; 
for  birdcages,  211. 

Fruit  dried  or  shrivelled,  experiments 
on  with  air-pump,  228. 

G. 

Galileo  rejects  the  ancient  doctrine  of  a 

vacuum,  190. 

Garnerin,  his  ascent  in  a  balloon,  265. 
Gas-holders,  212, 
Gasometers,  213. 
Gauge  of  air-pump,  224. 
Gay  Lussac,   his  ascent  in  a  balloon, 

265. 

Governor  sluice,  162. 
Guinea  and  feather  experiment,  232. 
Gun,  air,  257. 

H. 

Heat,  its  effects,  171. 
Heating  houses,  method  of,  87. 
Hydraulics,  130. 

Hydrogen  first  used  for  balloons,  262. 
Hydrometer,  Sikes's,  120 ;  Nicholson's, 

121 ;  De  Parcieux's,  122. 
Hydrostatic  press,  10  j  bellows,  12. 


Ice  lighter  than  water,  82. 

Jets  d'eau,  249. 

Immersion  of  solids  in  liquids,  58. 

Impenetrability  of  air  proved  experi- 
mentally, 179. 

Inertia  of  air,  its  effects,  177. 

Ink  bottles  to  prevent  ink  evaporating, 
210. 

K. 

Kettle,  form -of  its  spout,  41  ;  effect  in 
boiling,  209. 


Lana,  Francis,  his  balloon,  259. 

Level,  its  exact  meaning,  52. 

Leveling,  instruments  for,  54. 

Life  preservers,  79. 

Lifting  parnp,  238. 

Limits,  probable  ones  of  atmosph-ore, 
182. 

Liquids  machines,  8;  experiment  to 
prove  their  compression,  35  ;  main- 
tain their  level, 37;  their  surface  level, 
42 ;  resistance  of,  J.43. 

Liquors,  effervescing,  214. 

Locks  of  canals,  49. 

M. 

Machines,  hydraulic,  150  ;   for  raising 

water,  238. 
Magdeburg  hemispheres,  231. 


Matter,  its  mechanical  forms,  1. 
Mercury,  why  used  in  barometer,  197  ; 

method  of  purifying  it,  195. 
Mill,  Barker's,  156. 
Montgolfier,  his  balloon,  261. 

N. 

Nature  abhors  a  vacuum,  189. 
Nicholson's  hydrometer,  121. 

O. 

Oil  floats  on  water,  83. 

Oronoko,  river,  its  disappearance,  48. 

P. 

Parachute,  263. 

Paradox,  hydrostatic.  8. 

Pascal,  his  verification  of  Torricelli'g 
discovery  of  the  effects  of  atmospheric 
pressure,  191. 

Penetration  of  dimensions,  127. 

Pilatre  de  Rozier  ascends  in  a  balloon, 
262. 

Pneumatics,  169. 

Pneumatic  trough,  212. 

Pressure  of  liquids,  3  ;  hydrostatic,  ex- 
amples of,  in  animal  economy,  16  ; 
proportional  to  the  depth,  17 ;  equal 
in  all  directions,  21 ;  on  the  sides  of  a 
vessel,  23 ;  on  embankments,  26 ; 
greater  than  the  weight  which  pro- 
duces it,  27  ;  independent  of  the  shape 
of  the  vessel,  29. 

Proof,  spirit,  84. 

Pumps,  their  theory  discovered  by  Tor- 
ricelli,  191 ;  water  cannot  rise  in, 
without  atmospheric  pressure,  230 ; 
lifting,  238;  without  friction,  240; 
suction,  241  ;  forcing,  246 ;  double 
forcing,  250. 

R. 

Railroads,  their  advantages,  149. 

Rarefaction  of  air,  214. 

Regulation  of  mill-work  by  governor, 
162. 

Resistance  of  air,  its  effects,  177. 

Respiration  rightly  accounted  for  by  an 
ancient  writer,  190. 

Rivers,  their  origin  and  course  explain- 
ed, 46 ;  their  disappearance  explained, 
48  ;  eddies  of,  149 ;  flowing  through 
a  lake,  138. 

Rocks  split  by  the  pressure  of  liquids, 
36. 

-s. 

Scale  of  barometer,  194. 

Screw  of  Archimedes,  157. 

Ships,  their  form  explained,  76 ;  why 

they  lean  sidewards,  101. 
Sikes's  Hydrometer,  120. 
Siphon  gauge,  225;  Wurtemberg,  256. 
Sky,  its  color  accounted  for,  174 
Fluice,  governor,  162 


INDEX. 


273 


Solids  measured  by  immersion,  59. 

Sound  can  only  be  produced  in  air,  234. 

Specific  gravity,  102  ;  methods  of  find- 
ing it,  115;  of  a  mixture,  128. 

Spirit  level,  56. 

Spouting  fluids,  velocity  of,  131. 

Springs  explained  ;  submarine  ones  ex- 
plained, 47. 

Steam-boats,  use  of  movable  weights 
on  deck, 101. 

Suction,  ancient  theory  of,  wrong,  189. 

Suction  pump,  241. 

Syringe,  exhausting,  215 ;  condensing, 
234. 

T. 

Tea-pot,  form  ol  its  spout,  41 ;  why  a 
hole  in  the  lid  of,  209. 

Tequendama,  cataract  of,  47. 

Torricelli  accounts  for  the  elevation  ot 
water  in  pumps  ;  discovers  the  ba- 
rometer, 190. 

Toys,  philosophical  ones,  82. 

V. 

Vacuum,  ancient  doctrine  respecting, 


Vapor.  173. 

Vaporization,  173. 

Vena  contracta,  136. 

Vent-peg,  209. 

Vernier  applied  to  barometer,  200. 


Walking  on  water,  99. 

Water  apparently  converted  into  wine, 
85;  how  obtained  pure,  105;  wheel, 
overshot,  151 ,  undershot,  154;  breast, 
155. 

Waves,  optical  deception  of,  43  ;  causes 
of  this  appearance,  44. 

Weather-glass,  common  rules  absurd 
202  ;  correct  rules  of  it,  203. 

Weight  lost  by  immersion,  63  ;  of  air, 
176  ;  of  atmosphere  equal  to  its  elas- 
ticity, 187. 

Wells  of  water  explained,  47. 

Wheel  barometer,  198. 

Wind  arises  from  the  inertia  of  air,  178 ; 
its  effects,  179. 

Wine,  guggling  noise  in  decanting, 213  j 
error  in  the  common  method  of  cool- 
ing, 88. 

Wurtemberg  siphon,  256. 


THE    END. 


m 


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